A289162 Number of 4-cycles in the n X n black bishop graph.

0, 0, 0, 6, 39, 106, 321, 644, 1402, 2412, 4382, 6842, 11097, 16198, 24311, 33768, 47908, 64056, 87084, 112974, 148539, 188034, 240669, 298540, 373758, 455780, 560170, 673218, 814541, 966686, 1153971, 1354576, 1598216, 1858032, 2169880, 2501142, 2894607, 3311130

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 (2,3,-8,-2,12,-2,-8,3,2,-1).

Formula

a(n) = ((-1 + n)*(15 - 193*n + 162*n^2 - 68*n^3 + 12*n^4 - 15*(-1)^n*(1 - 7*n + 2*n^2)))/240.

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

G.f.: x^4*(6 + 27*x + 10*x^2 + 40*x^3 + 8*x^4 + 5*x^5) / ((1 - x)^6*(1 + x)^4). - Colin Barker, Jun 27 2017

Mathematica

Table[(n - 1) (15 - 193 n + 162 n^2 - 68 n^3 + 12 n^4 - 15 (-1)^n (2 n^2 - 7 n + 1))/240, {n, 20}]
LinearRecurrence[{2, 3, -8, -2, 12, -2, -8, 3, 2, -1}, {0, 0, 0, 6, 39, 106, 321, 644, 1402, 2412}, 20]

Prog

(PARI) concat(vector(3), Vec(x^4*(6 + 27*x + 10*x^2 + 40*x^3 + 8*x^4 + 5*x^5) / ((1 - x)^6*(1 + x)^4) + O(x^40))) \\ Colin Barker, Jun 27 2017

Crossrefs

Cf. A289161 (3-cycles), A289163 (5-cycles), A289160 (6-cycles).

Sequence in context: A354728 A220855 A351047 * A164081 A164082 A159571

Adjacent sequences: A289159 A289160 A289161 * A289163 A289164 A289165

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 26 2017

Status

approved