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A288918 Number of 4-cycles in the n X n king graph. 4
0, 3, 29, 79, 153, 251, 373, 519, 689, 883, 1101, 1343, 1609, 1899, 2213, 2551, 2913, 3299, 3709, 4143, 4601, 5083, 5589, 6119, 6673, 7251, 7853, 8479, 9129, 9803, 10501, 11223, 11969, 12739, 13533, 14351, 15193, 16059, 16949, 17863 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, King Graph
FORMULA
a(n) = 12*n^2 - 34*n + 23 for n > 1. - Andrew Howroyd, Jun 19 2017
From Colin Barker, Mar 11 2019: (Start)
G.f.: x^2*(3 + 20*x + x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. (End)
E.g.f.: exp(x)*(23 - 22*x + 12*x^2) - 23 - x. - Stefano Spezia, Aug 14 2022
MATHEMATICA
Table[If[n == 1, 0, 23 - 34 n + 12 n^2], {n, 20}]
Join[{0}, LinearRecurrence[{3, -3, 1}, {1, 3, 29}, {2, 20}]]
CoefficientList[Series[(-3 x - 20 x^2 - x^3)/(-1 + x)^3, {x, 0, 20}], x]
PROG
(PARI) a(n)=if(n, 12*n^2-10*n+1, 0) \\ Charles R Greathouse IV, Jun 19 2017
(PARI) concat(0, Vec(x^2*(3 + 20*x + x^2) / (1 - x)^3 + O(x^40))) \\ Colin Barker, Mar 11 2019
CROSSREFS
Cf. A016742 (3-cycles), A288919 (5-cycles), A288920 (6-cycles).
Sequence in context: A257293 A221745 A087210 * A190942 A106943 A281712
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 19 2017
STATUS
approved

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Last modified April 19 11:31 EDT 2024. Contains 371792 sequences. (Running on oeis4.)