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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 April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)