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

Offset: 1

Author

Ben Eck, Apr 20 2022

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A352994, A352847.

Programs

Python

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

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