Ben Eck - cp's OEIS frontend

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

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

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

Original entry on oeis.org

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

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

Original entry on oeis.org

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

Ben Eck, Apr 14 2022

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

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

Cf. A129002, A352847.

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

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

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

A352847 Number of copies of the star graph S(2,1,1) contained within the n-dimensional hypercube graph.

Original entry on oeis.org

0, 0, 48, 576, 3840, 19200, 80640, 301056, 1032192, 3317760, 10137600, 29736960, 84344832, 232587264, 626196480, 1651507200, 4278190080, 10909384704, 27433893888, 68136468480, 167352729600, 406931374080, 980510834688, 2343038877696, 5556613939200

Offset: 1

Ben Eck, Apr 05 2022

The star graph S(2,1,1) is the unique tree with degree sequence 3,2,1,1,1.

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Cf. A129002.

a[n_] := (2^n)*Binomial[n,2]*(n-1)*(n-2); Array[a, 25] (* Amiram Eldar, Apr 22 2022 *)

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

a(n) = 2^n*binomial(n,2)*(n-1)*(n-2).
G.f.: 48*x^3*(1 + 2*x)/(1 - 2*x)^5. - Stefano Spezia, Apr 15 2022
Sum_{n>=3} 1/a(n) = 9/8 + log(2)^2/2 - 3*log(2)/4 - Pi^2/12. - Amiram Eldar, Apr 22 2022

cp's OEIS Frontend

User: Ben Eck

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Python

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

Formula

A352847 Number of copies of the star graph S(2,1,1) contained within the n-dimensional hypercube graph.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

Formula