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

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

Table[Binomial[n + 1, 4] (-62 + 11 n - 109 n^2 + 40 n^3)/70, {n, 20}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 1, 57, 486, 2360, 8394, 24354}, 40]
CoefficientList[Series[(x^2 + 49 x^3 + 58 x^4 + 12 x^5)/(-1 + x)^8, {x, 0, 20}], x]

Prog

(PARI) a(n)=n*(40*n^6 - 189*n^5 + 189*n^4 + 105*n^3 - 105*n^2 + 84*n - 124)/1680 \\ Charles R Greathouse IV, Aug 10 2017

Crossrefs

Cf. A034827 (3-cycles), A051843 (4-cycles), A290775 (5-cycles).

Sequence in context: A184224 A337629 A218812 * A027143 A164786 A240416

Adjacent sequences: A290776 A290777 A290778 * A290780 A290781 A290782

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 10 2017

Status

approved