STATUS
reviewed
approved
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Revision History for A289163
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
proposed
reviewed
STATUS
editing
proposed
LINKS
Colin Barker, <a href="/A289163/b289163.txt">Table of n, a(n) for n = 1..1000</a>
FORMULA
G.f.: 2*x^34*(5 + 32*x + 57*x^2 + 146*x^3 + 19*x^4 + 104*x^5 + 15*x^6 + 6*x^7) / ((1 - x)^7*(1 + x)^5). - Colin Barker, Jun 27 2017
PROG
(PARI) concat(vector(3), Vec(2*x^34*(5 + 32*x + 57*x^2 + 146*x^3 + 19*x^4 + 104*x^5 + 15*x^6 + 6*x^7) / ((1 - x)^7*(1 + x)^5) + O(x^40))) \\ Colin Barker, Jun 27 2017
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
LINKS
<a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-10,-5,20,0,-20,5,10,-4,-2,1).
FORMULA
a(n) = 2*a(n-1)+4*a(n-2)-10*a(n-3)-5*a(n-4)+20*a(n-5)-20*a(n-7)+5*a(n-8)+10*a(n-9)-4*a(n-10)-2*a(n-11)++a(n-12).
G.f.: 2*x^3*(5 + 32*x + 57*x^2 + 146*x^3 + 19*x^4 + 104*x^5 + 15*x^6 + 6*x^7) / ((1 - x)^7*(1 + x)^5). - Colin Barker, Jun 27 2017
PROG
(PARI) concat(vector(3), Vec(2*x^3*(5 + 32*x + 57*x^2 + 146*x^3 + 19*x^4 + 104*x^5 + 15*x^6 + 6*x^7) / ((1 - x)^7*(1 + x)^5) + O(x^40))) \\ Colin Barker, Jun 27 2017
KEYWORD
nonn,changed,easy
STATUS
proposed
editing
STATUS
editing
proposed
NAME
allocated for Eric W. Weisstein
Number of 5-cycles in the n X n black bishop graph.
DATA
0, 0, 0, 10, 84, 322, 1172, 2780, 7016, 13532, 27720, 47318, 84796, 133294, 217756, 322392, 492240, 696216, 1009680, 1377474, 1918500, 2541946, 3426852, 4431988, 5816888, 7371572, 9460568, 11782862, 14837004, 18204326, 22551340, 27310384, 33355168, 39932592, 48168480
OFFSET
1,4
LINKS
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BlackBishopGraph.html">Black Bishop Graph</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
FORMULA
a(n) = (-165 - 282*n + 972*n^2 - 730*n^3 + 280*n^4 - 68*n^5 + 8*n^6 - 5*(-1)^n*(-33 - 26*n + 96*n^2 - 46*n^3 + 6*n^4))/240.
a(n) = 2*a(n-1)+4*a(n-2)-10*a(n-3)-5*a(n-4)+20*a(n-5)-20*a(n-7)+5*a(n-8)+10*a(n-9)-4*a(n-10)-2*a(n-11)++a(n-12).
MATHEMATICA
Table[(-165 - 282 n + 972 n^2 - 730 n^3 + 280 n^4 - 68 n^5 + 8 n^6 - 5 (-1)^n (-33 - 26 n + 96 n^2 - 46 n^3 + 6 n^4))/240, {n, 20}]
LinearRecurrence[{2, 4, -10, -5, 20, 0, -20, 5, 10, -4, -2, 1}, {0, 0, 0, 10, 84, 322, 1172, 2780, 7016, 13532, 27720, 47318}, 20]
KEYWORD
allocated
nonn
AUTHOR
Eric W. Weisstein, Jun 26 2017
STATUS
approved
editing