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A290029 Number of 6-cycles in the n-halved cube graph. 3
0, 0, 0, 640, 34720, 533760, 4735360, 30822400, 164183040, 759521280, 3163607040, 12148899840, 43724595200, 149243494400, 487404503040, 1533406085120, 4672095518720, 13845292646400, 40043324375040, 113352785264640, 314803035832320, 859445521285120 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 07:18 EST 2018. Contains 297787 sequences.