A352994 Number of copies of the star graph S(2,2,1) contained within the n-dimensional hypercube graph.

0, 0, 72, 1536, 14400, 92160, 470400, 2064384, 8128512, 29491200, 100362240, 324403200, 1005109248, 3005743104, 8722022400, 24662507520, 68183654400, 184817811456, 492285984768, 1291006771200, 3338686955520, 8526181171200, 21526669688832, 53788022931456

Offset: 1

Author

Ben Eck, Apr 14 2022

Keywords

• easy
• nonn

Comments

S(2,2,1) is the star graph with two legs of length two and one of length one.

Links

• Index entries for linear recurrences with constant coefficients, signature (12,-60,160,-240,192,-64).

Crossrefs

Cf. A129002, A352847.

Programs

Mathematica

a[n_] := (2^n)*Binomial[n,3]*3*n*(n-2); Array[a, 24] (* Amiram Eldar, Apr 22 2022 *)

Python

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

Formula

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

G.f.: 24*x^3*(3 + 28*x + 12*x^2)/(1 - 2*x)^6. - Stefano Spezia, Apr 15 2022

Sum_{n>=3} 1/a(n) = 13/32 + 3*log(2)^2/16 - log(2)/4 - Pi^2/32. - Amiram Eldar, Apr 22 2022