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A290779

Number of 6-cycles in the n-triangular honeycomb bishop graph.

0, 0, 1, 57, 486, 2360, 8394, 24354, 61104, 137412, 283635, 546403, 994422, 1725516, 2875028, 4625700, 7219152, 10969080, 16276293, 23645709, 33705430, 47228016, 65154078, 88618310, 118978080, 157844700, 207117495, 269020791, 346143942, 441484516, 558494760

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..31.

Eric Weisstein's World of Mathematics, Graph Cycle

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

a(n) = binomial(n + 1, 4)*(-62 + 11*n - 109*n^2 + 40*n^3)/70.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

G.f.: (x (x^2 + 49 x^3 + 58 x^4 + 12 x^5))/(-1 + x)^8.

MATHEMATICA