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URL: https://oeis.org/A289163

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A289163
Number of 5-cycles in the n X n black bishop graph.
4
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, Black Bishop Graph
Eric Weisstein's World of Mathematics, Graph Cycle
Index entries for linear recurrences with constant coefficients, signature (2,4,-10,-5,20,0,-20,5,10,-4,-2,1).
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).
G.f.: 2*x^4*(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
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]
PROG
(PARI) concat(vector(3), Vec(2*x^4*(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
CROSSREFS
Cf. A289161 (3-cycles), A289162 (4-cycles), A289160 (6-cycles).
Sequence in context: A271557 A351750 A267031 * A092718 A090763 A016131
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 26 2017
STATUS
approved