A352102 Number of graph minors of the n-centipede graph.

3, 11, 33, 95, 268, 767, 2196, 6347, 18392, 53465, 155437, 451938, 1312136, 3803893, 11005162, 31774289, 91539282, 263158830, 754942580, 2161397128, 6176051375, 17615054467, 50152259705, 142550610355, 404534021375, 1146259423759, 3243280480390, 9164103218022, 25859923641625, 72882368515277

Offset

1,1

Comments

Counts exclude the null graph.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Centipede Graph.

Eric Weisstein's World of Mathematics, Graph Minor.

Prog

(PARI) \\ G() is g.f. of connected subgraphs: x counting number of centipede segments required and y counting number of unused single vertices. Excludes single vertex.
EulerMTS(p)={my(n=serprec(p, x)-1, vars=variables(p)); exp(sum(i=1, n, substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i))}
G() = x*(1 - x - (3 + y^2)*x^2 + (2 - y)*(1 + y^2)*x^3 + (1 + y^2)*x^4 + (1 - 3*y + y^2 - y^3 + y^4)*y*x^5 - (1 - y^2)*y^2*x^6 + (1 - y)*y^4*x^7)/((1 - (2 + y)*x + y*x^2)*(1 - (2 + y^2)*x^2 + y^2*x^4))
seq(n) = {my(p=EulerMTS(G() + O(x*x^n))); Vec(subst(deriv(y*p/(1 - x*y^2), y), y, 1) - 1/(1-x))} \\ Andrew Howroyd, Jun 20 2025

Crossrefs

Sequence in context: A079996 A288038 A186308 * A171270 A182879 A124640

Adjacent sequences: A352099 A352100 A352101 * A352103 A352104 A352105

Keyword

nonn

Author

Eric W. Weisstein, May 06 2022

Extensions

a(11) onwards from Andrew Howroyd, Jun 20 2025

Status

approved