A290027 Number of 4-cycles in the n-halved cube graph.

0, 0, 3, 102, 900, 5160, 23520, 92736, 330624, 1094400, 3421440, 10222080, 29432832, 82188288, 223641600, 595230720, 1554186240, 3990749184, 10097197056, 25214976000, 62234296320, 151993712640, 367691563008, 881823055872, 2098200576000, 4956409036800

Offset

1,3

Links

Table of n, a(n) for n=1..26.

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 (10, -40, 80, -80, 32).

Formula

a(n) = 3*2^(n-5)*binomial(n,3)*(13*n-35).

a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5).

G.f.: (-3*x*(x^2 + 24*x^3))/(-1 + 2*x)^5.

Mathematica

Table[3 2^(n - 5) Binomial[n, 3] (13 n - 35), {n, 20}]
LinearRecurrence[{10, -40, 80, -80, 32}, {0, 0, 3, 102, 900}, 20]
CoefficientList[Series[-((3 (x^2 + 24 x^3))/(-1 + 2 x)^5), {x, 0, 20}], x]

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 32, -80, 80, -40, 10]^(n-1)*[0; 0; 3; 102; 900])[1, 1] \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Cf. A290026 (3-cycles), A290028 (5-cycles), A290029 (6-cycles).

Sequence in context: A108220 A130733 A037062 * A224817 A157549 A157566

Adjacent sequences: A290024 A290025 A290026 * A290028 A290029 A290030

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 17 2017

Status

approved