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

%I #29 May 22 2022 14:14:50

%S 0,0,16,1152,16640,140800,887040,4616192,20987904,86261760,327782400,

%T 1169653760,3964207104,12869828608,40285306880,122211532800,

%U 360794030080,1040028008448,2935426646016,8130951905280,22146344550400,59411980615680,157208570494976

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

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

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (14,-84,280,-560,672,-448,128).

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

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

%o (Python) from math import comb

%o def a(n):

%o return (2**n)*comb(n,3)*((n-1)**3-3*(n-1))

%Y Cf. A352994, A352847.

%K nonn,easy

%O 1,3

%A _Ben Eck_, Apr 20 2022