A290028 Number of 5-cycles in the n-halved cube graph.

0, 0, 0, 288, 5664, 50688, 314496, 1569792, 6773760, 26320896, 94482432, 318726144, 1022681088, 3148873728, 9366110208, 27051687936, 76178522112, 209845223424, 566967140352, 1505815953408, 3938646491136, 10161657741312, 25894399770624, 65248539181056

Offset

1,4

Links

Table of n, a(n) for n=1..24.

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 (12, -60, 160, -240, 192, -64).

Formula

a(n) = 3*2^n*binomial(n,4)*(29*n-86)/5.

a(n) = 12*a(n-1)-60*a(n-2)+160*a(n-3)-240*a(n-4)+192*a(n-5)-64*a(n-6).

G.f.: (96*x*(3*x^3 + 23*x^4))/(-1 + 2*x)^6.

Mathematica

Table[3 2^n Binomial[n, 4] (29 n - 86)/5, {n, 20}]
LinearRecurrence[{12, -60, 160, -240, 192, -64}, {0, 0, 0, 288, 5664, 50688}, 20]
CoefficientList[Series[(96 (3 x^3 + 23 x^4))/(-1 + 2 x)^6, {x, 0, 20}], x]

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -64, 192, -240, 160, -60, 12]^(n-1)*[0; 0; 0; 288; 5664; 50688])[1, 1] \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Cf. A290026 (3-cycles), A290027 (4-cycles), A290029 (6-cycles).

Sequence in context: A229506 A332429 A232340 * A330817 A299860 A264204

Adjacent sequences: A290025 A290026 A290027 * A290029 A290030 A290031

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 17 2017

Status

approved