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A288919 Number of 5-cycles in the n X n king graph. 4
0, 0, 52, 176, 372, 640, 980, 1392, 1876, 2432, 3060, 3760, 4532, 5376, 6292, 7280, 8340, 9472, 10676, 11952, 13300, 14720, 16212, 17776, 19412, 21120, 22900, 24752, 26676, 28672 (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

a(n) = 36*n^2 - 128*n + 112 for n>1. - Andrew Howroyd, Jun 19 2017

From Colin Barker, Mar 11 2019: (Start)

G.f.: 4*x^3*(13 + 5*x) / (1 - x)^3.

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

(End)

MATHEMATICA

Table[If[n == 1, 0, 4 (n - 2) (9 n - 14)], {n, 30}]

Join[{0, 0}, LinearRecurrence[{3, -3, 1}, {20, 0, 52}, {3, 20}]]

CoefficientList[Series[-((4 x^2 (13 + 5 x))/(-1 + x)^3), {x, 0, 20}], x]

PROG

(PARI) a(n)=if(n<3, 0, 36*n^2-128*n+112) \\ Charles R Greathouse IV, Jun 19 2017

(PARI) concat([0, 0], Vec(4*x^3*(13 + 5*x) / (1 - x)^3 + O(x^40))) \\ Colin Barker, Mar 11 2019

CROSSREFS

Cf. A016742 (3-cycles), A288918 (4-cycles), A288920 (6-cycles).

Sequence in context: A292172 A166390 A161478 * A260549 A211564 A251287

Adjacent sequences:  A288916 A288917 A288918 * A288920 A288921 A288922

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jun 19 2017

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)