A289160 Number of 6-cycles in the n X n black bishop graph.

0, 0, 0, 15, 220, 1253, 5412, 15642, 44368, 97158, 218816, 410209, 797052, 1350435, 2367668, 3733284, 6068736, 9065724, 13907808, 19916451, 29188092, 40399953, 57056164, 76789790, 105186576, 138276450, 184618720, 237885141, 310761308, 393568879, 504579828

Offset

1,4

Links

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

Eric Weisstein's World of Mathematics, Black Bishop Graph

Eric Weisstein's World of Mathematics, Graph Cycle

Index entries for linear recurrences with constant coefficients, signature (2,5,-12,-9,30,5,-40,5,30,-9,-12,5,2,-1).

Formula

a(n) = 2*a(n-1)+5*a(n-2)-12*a(n-3)-9*a(n-4)+30*a(n-5)+5*a(n-6)-40*a(n-7)+5*a(n-8)+30*a(n-9)-9*a(n-10)-12*a(n-11)+5*a(n-12)+2*a(n-13)-a(n-14).

G.f.: x^4*(15 + 190*x + 738*x^2 + 1986*x^3 + 1328*x^4 + 2590*x^5 - 242*x^6 + 982*x^7 + 81*x^8 + 12*x^9) / ((1 - x)^8*(1 + x)^6). - Colin Barker, Jun 27 2017

Mathematica

Table[(20580 - 15312 n - 27027 n^2 + 28840 n^3 - 10850 n^4 + 2772 n^5 - 658 n^6 + 80 n^7 - 35 (-1)^n (-7 + 2 n) (-84 + 32 n + 83 n^2 - 46 n^3 + 6 n^4))/3360, {n, 20}]
LinearRecurrence[{2, 5, -12, -9, 30, 5, -40, 5, 30, -9, -12, 5, 2, -1}, {0, 0, 0, 15, 220, 1253, 5412, 15642, 44368, 97158, 218816, 410209, 797052, 1350435}, 20]

Prog

(PARI) concat(vector(3), Vec(x^4*(15 + 190*x + 738*x^2 + 1986*x^3 + 1328*x^4 + 2590*x^5 - 242*x^6 + 982*x^7 + 81*x^8 + 12*x^9) / ((1 - x)^8*(1 + x)^6) + O(x^40))) \\ Colin Barker, Jun 27 2017

Crossrefs

Cf. A289161 (3-cycles), A289162 (4-cycles), A289163 (5-cycles).

Sequence in context: A152272 A091644 A238538 * A027843 A027840 A279530

Adjacent sequences: A289157 A289158 A289159 * A289161 A289162 A289163

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 26 2017

Status

approved