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A290779 Number of 6-cycles in the n-triangular honeycomb bishop graph. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 21:55 EDT 2022. Contains 356016 sequences. (Running on oeis4.)