A352994 -id:A352994 - cp's OEIS frontend

A351632 Number of copies of the star graph S(2,1,1,1) contained in the n-dimensional hypercube graph.

0, 0, 0, 192, 2560, 19200, 107520, 501760, 2064384, 7741440, 27033600, 89210880, 281149440, 852819968, 2504785920, 7156531200, 19964887040, 54546923520, 146314100736, 386106654720, 1004116377600, 2577232035840, 6536738897920, 16401272143872, 40748502220800

Offset: 1

Ben Eck, May 04 2022

The star graph S(2,1,1,1) is the unique tree with degree sequence 4,2,1,1,1,1.

Amiram Eldar, Table of n, a(n) for n = 1..3266
Index entries for linear recurrences with constant coefficients, signature (12,-60,160,-240,192,-64).

Cf. A352847, A352994, A353029.

a[n_] := 2^n * Binomial[n, 3] * (n - 1) * (n - 3); Array[a, 25] (* Amiram Eldar, May 23 2022 *)

a(n) = 2^n*binomial(n,3)*(n-1)*(n-3); \\ Michel Marcus, May 23 2022

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

a(n) = 2^n*binomial(n,3)*(n-1)*(n-3).
G.f.: 64*x^4*(3 + 4*x)/(1 - 2*x)^6. - Stefano Spezia, May 20 2022
Sum_{n>=4} 1/a(n) = Pi^2/8 + 17*log(2)/16 - 3*log(2)^2/4 - 77/48. - Amiram Eldar, May 23 2022

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

Original entry on oeis.org

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

Ben Eck, Apr 20 2022

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

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

Cf. A352994, A352847.

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

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

cp's OEIS Frontend

A351632 Number of copies of the star graph S(2,1,1,1) contained in the n-dimensional hypercube graph.

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