A290029 Number of 6-cycles in the n-halved cube graph.

0, 0, 0, 640, 34720, 533760, 4735360, 30822400, 164183040, 759521280, 3163607040, 12148899840, 43724595200, 149243494400, 487404503040, 1533406085120, 4672095518720, 13845292646400, 40043324375040, 113352785264640, 314803035832320, 859445521285120

Offset

1,4

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Halved Cube Graph

Index entries for linear recurrences with constant coefficients, signature (14, -84, 280, -560, 672, -448, 128).

Formula

a(n) = 2^n*binomial(n, 4)*(81*n^2 - 552*n + 952).

a(n) = 14*a(n-1)-84*a(n-2)+280*a(n-3)-560*a(n-4)+672*a(n-5)-448*a(n-6)+128*a(n-7).

G.f.: (-160*x*(4*x^3 + 161*x^4 + 634*x^5))/(-1 + 2*x)^7.

Mathematica

seq = Table[2^n Binomial[n, 4] (81 n^2 - 552 n + 952), {n, 30}]
LinearRecurrence[{14, -84, 280, -560, 672, -448, 128}, {0, 0, 0, 640, 34720, 533760, 4735360}, 20]
CoefficientList[
Series[-((160 (4 x^3 + 161 x^4 + 634 x^5))/(-1 + 2 x)^7), {x, 0,
   20}], x]

Crossrefs

Cf. A290026 (3-cycles), A290027 (4-cycles), A290028 (5-cycles).

Sequence in context: A233911 A178975 A170774 * A268875 A252426 A256777

Adjacent sequences: A290026 A290027 A290028 * A290030 A290031 A290032

Keyword

nonn

Author

Eric W. Weisstein, Jul 17 2017

Status

approved