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A288919
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Number of 5-cycles in the n X n king graph.
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4
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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;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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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).
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FORMULA
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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)
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MATHEMATICA
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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]
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, Jun 19 2017
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STATUS
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approved
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