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Revision History for A232060

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A232060

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.
(history; published version)

#8 by Bruno Berselli at Wed Oct 03 05:54:47 EDT 2018

STATUS

proposed

approved

#7 by Colin Barker at Wed Oct 03 05:48:03 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Wed Oct 03 05:47:46 EDT 2018

NAME

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.

#5 by Colin Barker at Wed Oct 03 05:47:10 EDT 2018

NAME

Number of nX3 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

COMMENTS

Column 3 of A232065

FORMULA

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

EXAMPLE

Some solutions for n=7:

CROSSREFS

Column 3 of A232065.

STATUS

approved

editing

#4 by R. H. Hardin at Sun Nov 17 13:54:57 EST 2013

STATUS

editing

approved

#3 by R. H. Hardin at Sun Nov 17 13:54:52 EST 2013

LINKS

R. H. Hardin, <a href="/A232060/b232060.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Sun Nov 17 13:54:19 EST 2013

NAME

allocated for R. H. Hardin

Number of nX3 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

DATA

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

OFFSET

1,1

COMMENTS

Column 3 of A232065

FORMULA

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)

EXAMPLE

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Nov 17 2013

STATUS

approved

editing

#1 by R. H. Hardin at Sun Nov 17 13:51:39 EST 2013

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved