OFFSET
1,2
COMMENTS
The wheel graph is defined for n >= 4. The sequence has been extended to n=1 to include all non-null graphs on at most n nodes (paths and C_3), since these graphs are minors of every wheel. - Andrew Howroyd, Jun 18 2025
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Andrew Howroyd, Derivation of formula, Jun 2025.
Eric Weisstein's World of Mathematics, Graph Minor.
Eric Weisstein's World of Mathematics, Wheel Graph.
PROG
(PARI) \\ DIK is unlabeled bracelet transform.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
DIK(p, n)={(sum(d=1, n, eulerphi(d)/d*log(subst(1/(1+O(x*x^(n\d))-p), x, x^d))) + ((1+p)^2/(1-subst(p, x, x^2))-1)/2)/2}
seq(n)={ my(A=O(x*x^n),
gc = x^2*(1 + x + x^2 + 2*x^3 + 2*x^5 - x^7 - x^8 - 2*x^9)/((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)),
gw = x*(DIK(x/(1 - x), n) - x*(1 + x)/(1 - x)),
gb = x^2*Ser(EulerT(Vec(x*(1 - x - x^2)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)) + A))));
Vec(((1 + gb - gc)/eta(x + A) + gw - 1)/(1 - x));
} \\ Andrew Howroyd, Jun 18 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 30 2022
EXTENSIONS
a(12) from Eric W. Weisstein, Mar 15 2023
a(13)-a(18) from Eric W. Weisstein, Oct 11-20 2023
a(1)-a(3) prepended and a(19) onwards from Andrew Howroyd, Jun 18 2025
STATUS
approved