OFFSET
1,1
COMMENTS
Counts exclude the null graph.
The n-sunlet graph is defined for n >= 3. The sequence has been extended to n = 1 using the formula. - Andrew Howroyd, Jun 20 2025
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Graph Minor.
Eric Weisstein's World of Mathematics, Sunlet Graph.
PROG
(PARI) \\ Compare A352102, B(n) gives subgraphs that are not trees as g.f.
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))}
B(n)={(sum(d=1, n, eulerphi(d)/d*log(1/(1-x^d*(y^d+1/(1-x^d))) + O(x*x^n))) + ( (1+x*(y+1/(1-x)))^2/(1-x^2*(y^2 + 1/(1-x^2)))-1)/2)/2 - x*(y+1/(1-x)) - x^2*((y+1/(1-x))^2 + y^2+1/(1-x^2))/2}
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*B(n)/(1 - x*y), y), y, 1) - 1/(1-x))} \\ Andrew Howroyd, Jun 20 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 02 2022
EXTENSIONS
a(12) from Eric W. Weisstein, Dec 04 2024
a(1)-a(2) prepended and a(13) onwards from Andrew Howroyd, Jun 20 2025
STATUS
approved
