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A288920 Number of 6-cycles in the n X n king graph. 4
0, 0, 82, 430, 1030, 1882, 2986, 4342, 5950, 7810, 9922, 12286, 14902, 17770, 20890, 24262, 27886, 31762, 35890, 40270, 44902, 49786, 54922, 60310, 65950, 71842, 77986, 84382, 91030, 97930, 105082, 112486, 120142, 128050, 136210, 144622, 153286, 162202 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, King Graph

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

From Colin Barker, Jun 19 2017: (Start)

G.f.: 2*x^3*(41 + 92*x - 7*x^2) / (1 - x)^3.

a(n) = 550 - 534*n + 126*n^2 for n>2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)

MATHEMATICA

Table[If[n < 3, 0, 2 (275 - 267 n + 63 n^2)], {n, 20}]

CoefficientList[Series[(2 x^2 (-41 - 92 x + 7 x^2))/(-1 + x)^3, {x, 0, 20}], x]

Join[{0, 0}, LinearRecurrence[{3, -3, 1}, {142, -14, 82}, {3, 20}]]

PROG

(PARI) concat(vector(2), Vec(2*x^3*(41 + 92*x - 7*x^2) / (1 - x)^3 + O(x^50))) \\ Colin Barker, Jun 19 2017

(PARI) a(n)=if(n>2, 126*n^2-534*n+550, 0) \\ Charles R Greathouse IV, Jun 19 2017

CROSSREFS

Cf. A016742 (number of 3-cycles).

Cf. A288918 (number of 4-cycles).

Cf. A288919 (number of 5-cycles).

Sequence in context: A031696 A005972 A082972 * A304416 A316241 A305951

Adjacent sequences:  A288917 A288918 A288919 * A288921 A288922 A288923

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jun 19 2017

EXTENSIONS

More terms from Colin Barker, Jun 19 2017

STATUS

approved

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Last modified October 14 09:25 EDT 2019. Contains 327995 sequences. (Running on oeis4.)