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

1,3

Comments

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

Links

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

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A129002, A352847.

Sequence in context: A292881 A282018 A037251 * A234209 A280807 A268749

Adjacent sequences: A352991 A352992 A352993 * A352995 A352996 A352997

Keyword

easy,nonn

Author

Ben Eck, Apr 14 2022

Status

approved