A353029 Number of copies of the star graph S(2,2,2) contained in the n-dimensional hypercube graph.

0, 0, 16, 1152, 16640, 140800, 887040, 4616192, 20987904, 86261760, 327782400, 1169653760, 3964207104, 12869828608, 40285306880, 122211532800, 360794030080, 1040028008448, 2935426646016, 8130951905280, 22146344550400, 59411980615680, 157208570494976, 410812816556032, 1061313262387200

Offset

1,3

Comments

S(2,2,2) is the star graph with three legs of length two.

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 2^n*C(n,3)*((n-1)^3 - 3*(n-1)).

G.f.: 16*x^3*(1 + 58*x + 116*x^2 + 8*x^3)/(1 - 2*x)^7. - Stefano Spezia, Apr 20 2022

Mathematica

A353029[n_] := 2^n*Binomial[n, 3]*((n-1)^3 - 3*(n-1));
Array[A353029, 25] (* Paolo Xausa, Jun 29 2026 *)

Prog

(Python) from math import comb
def a(n):
    return (2**n)*comb(n, 3)*((n-1)**3-3*(n-1))

Crossrefs

Cf. A352994, A352847.

Sequence in context: A209541 A374493 A279295 * A053903 A254333 A102807

Adjacent sequences: A353026 A353027 A353028 * A353030 A353031 A353032

Keyword

nonn,easy

Author

Ben Eck, Apr 20 2022

Extensions

More terms from Paolo Xausa, Jun 29 2026

Status

approved