Search: a232065 -id:a232065
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A232059
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Number of n X 2 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal.
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+10
1
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2, 6, 14, 30, 66, 146, 322, 710, 1566, 3454, 7618, 16802, 37058, 81734, 180270, 397598, 876930, 1934130, 4265858, 9408646, 20751422, 45768702, 100946050, 222643522, 491055746, 1083057542, 2388758606, 5268572958, 11620203458, 25629165522
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) + a(n-3).
Empirical g.f.: 2*x*(1 + x + x^2) / (1 - 2*x - x^3). - Colin Barker, Oct 03 2018
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EXAMPLE
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Some solutions for n=7:
..0..1....2..1....2..1....2..1....1..2....0..1....1..2....2..1....0..1....0..1
..1..2....1..0....1..0....1..0....0..1....1..2....0..1....1..0....1..2....1..2
..0..1....0..1....2..1....2..1....1..0....0..1....1..2....0..1....0..1....0..1
..2..0....1..2....1..2....1..0....2..1....2..0....0..1....1..2....2..0....1..2
..0..1....2..0....2..1....2..1....1..0....1..2....2..0....2..1....1..2....2..1
..1..2....0..1....1..2....1..2....2..1....2..1....1..2....1..2....0..1....1..2
..0..1....1..2....0..1....2..1....1..2....1..0....2..1....2..1....1..2....2..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A232060
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Number of n X 3 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal.
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+10
1
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4, 14, 46, 130, 410, 1194, 3722, 10942, 33806, 100142, 307418, 915594, 2797794, 8365310, 25477518, 76390718, 232103802, 697334282, 2115143362, 6363967678, 19279364750, 58067541662, 175757663194, 529761502474, 1602452666114
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internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = a(n-1) + 7*a(n-2) - 3*a(n-3) + 3*a(n-4) - 7*a(n-5) + 2*a(n-6) - 2*a(n-7) + 2*a(n-8).
Empirical g.f.: 2*x*(1 + x + x^2)*(2 + 3*x - 3*x^2 - x^3 - 2*x^4 + 2*x^5) / (1 - x - 7*x^2 + 3*x^3 - 3*x^4 + 7*x^5 - 2*x^6 + 2*x^7 - 2*x^8). - Colin Barker, Oct 03 2018
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EXAMPLE
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Some solutions for n=7:
..2..0..2....0..1..0....0..1..2....2..1..0....1..2..1....1..2..1....1..2..1
..0..1..0....1..2..1....2..0..1....1..0..1....0..1..0....2..1..0....0..1..0
..1..2..1....2..1..2....0..2..0....2..1..2....1..2..1....1..0..1....1..0..1
..2..1..0....1..2..1....1..0..1....1..0..1....2..1..2....0..1..2....2..1..2
..0..2..1....0..1..2....2..1..2....0..1..2....1..2..1....2..0..1....1..0..1
..1..0..2....1..2..1....1..0..1....1..2..1....0..1..2....1..2..0....0..1..0
..2..1..0....0..1..0....2..1..2....2..1..2....1..2..1....2..1..2....1..2..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A232061
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Number of nX4 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal
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+10
1
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6, 30, 130, 534, 2230, 9310, 38870, 162278, 677510, 2828606, 11809446, 49304494, 205846518, 859410282, 3588042398, 14980095674, 62541977366, 261113080850, 1090148470882, 4551375536978, 19002016543538, 79333517919430
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internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 4*a(n-1) +a(n-2) -4*a(n-4) -3*a(n-5) +a(n-7) +3*a(n-8) -a(n-11)
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EXAMPLE
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Some solutions for n=7
..1..0..1..2....0..1..0..1....1..2..1..0....2..0..1..2....2..1..2..1
..2..1..0..1....1..2..1..2....0..1..0..2....0..2..0..1....1..2..1..0
..1..2..1..0....2..1..2..1....1..0..2..1....1..0..1..0....2..1..2..1
..2..0..2..1....1..0..1..2....2..1..0..2....2..1..2..1....1..2..1..0
..0..1..0..2....2..1..0..1....1..2..1..0....0..2..1..2....2..1..2..1
..1..2..1..0....1..2..1..2....2..1..2..1....1..0..2..1....1..2..1..0
..2..1..0..2....0..1..2..1....1..0..1..2....2..1..0..2....0..1..2..1
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A232062
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Number of nX5 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal
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+10
1
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10, 66, 410, 2230, 13538, 75462, 457234, 2561258, 15454594, 86936482, 522543518, 2950310558, 17671662754, 100103295530, 597736686594, 3395879611978, 20221409303002, 115182855491730, 684186672548350, 3906272828605434
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refs;
listen;
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text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) +30*a(n-2) -47*a(n-3) +39*a(n-4) -191*a(n-5) +159*a(n-6) -134*a(n-7) +378*a(n-8) -242*a(n-9) +203*a(n-10) -439*a(n-11) +179*a(n-12) -147*a(n-13) +281*a(n-14) -62*a(n-15) +49*a(n-16) -87*a(n-17) +8*a(n-18) -6*a(n-19) +10*a(n-20) for n>22
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EXAMPLE
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Some solutions for n=6
..2..1..2..1..0....0..2..0..1..0....2..1..0..2..0....2..1..2..1..2
..1..0..1..2..1....1..0..1..2..1....1..0..1..0..1....1..2..1..2..1
..0..1..2..1..2....2..1..2..1..0....0..1..2..1..2....2..1..0..1..2
..2..0..1..0..1....1..2..1..2..1....1..2..1..2..1....1..2..1..2..1
..1..2..0..1..2....2..1..2..1..0....2..1..2..1..0....2..1..0..1..0
..0..1..2..0..1....1..2..1..2..1....1..0..1..2..1....1..0..1..2..1
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A232063
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Number of nX6 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal
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+10
1
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16, 146, 1194, 9310, 75462, 612364, 4990482, 40661766, 331554282, 2703411654, 22045643128, 179775318402, 1466041167494, 11955330672874, 97494132143426, 795051433770004, 6483540298615466, 52872418589641126, 431167661161162982
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 8*a(n-1) +8*a(n-2) -48*a(n-3) -14*a(n-4) -398*a(n-5) +433*a(n-6) -478*a(n-7) +2797*a(n-8) -2080*a(n-9) +3344*a(n-10) -10791*a(n-11) +6352*a(n-12) -11493*a(n-13) +26807*a(n-14) -11133*a(n-15) +26275*a(n-16) -39528*a(n-17) +11642*a(n-18) -40057*a(n-19) +29717*a(n-20) -9677*a(n-21) +35669*a(n-22) -5207*a(n-23) +10008*a(n-24) -12233*a(n-25) -8213*a(n-26) -10936*a(n-27) -6439*a(n-28) +6651*a(n-29) +8825*a(n-30) +7963*a(n-31) -2212*a(n-32) -4693*a(n-33) -2951*a(n-34) +362*a(n-35) +1560*a(n-36) +417*a(n-37) -25*a(n-38) -294*a(n-39) -9*a(n-40) +24*a(n-42)
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EXAMPLE
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Some solutions for n=5
..0..1..2..1..2..1....1..2..1..2..1..0....2..1..2..1..0..1....1..0..1..2..0..1
..1..2..1..0..1..2....2..1..2..1..0..2....1..2..1..2..1..2....2..1..2..0..1..2
..0..1..2..1..0..1....1..0..1..0..2..1....2..1..0..1..0..1....1..2..0..1..0..1
..1..2..1..0..1..2....0..1..2..1..0..2....1..0..1..0..2..0....2..0..1..2..1..2
..2..1..2..1..2..1....1..2..1..0..2..1....2..1..2..1..0..2....1..2..0..1..2..1
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A232064
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Number of nX7 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal
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+10
1
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26, 322, 3722, 38870, 457234, 4990482, 59448262, 653375842, 7789998594, 85859588738, 1022554161202, 11291242022918, 134275256384066, 1485073515174330, 17633927192912362, 195323094382344414
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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Some solutions for n=4
..0..1..2..1..2..1..0....1..2..1..0..2..0..2....1..2..1..2..1..2..1
..1..0..1..0..1..2..1....0..1..2..1..0..1..0....2..1..0..1..0..1..0
..2..1..0..1..2..1..0....1..0..1..0..1..2..1....1..2..1..0..1..2..1
..1..0..2..0..1..2..1....2..1..0..2..0..1..0....2..1..2..1..2..1..2
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A232058
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Number of n X n 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal
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+10
0
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1, 6, 46, 534, 13538, 612364, 59448262, 10508498862, 4011743077182, 2813378775175894, 4273709472166465256, 11960135034686739832398
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graph;
refs;
listen;
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internal format)
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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Some solutions for n=5
..2..0..1..2..1....2..1..0..2..1....1..2..1..0..2....2..1..0..2..0
..0..1..2..1..0....1..2..1..0..2....0..1..0..1..0....1..0..2..0..1
..1..2..1..0..1....0..1..2..1..0....1..2..1..2..1....0..2..0..1..2
..2..1..0..1..2....1..2..1..2..1....0..1..0..1..0....2..0..1..2..1
..1..0..1..2..1....2..1..0..1..2....1..2..1..2..1....1..2..0..1..2
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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