cp's OEIS Frontend

A353209 Number of graph minors in the n-node wheel graph.

%I A353209 #39 Jun 19 2025 10:10:39
%S A353209 1,3,7,18,46,122,326,863,2252,5757,14430,35531,86215,206613,490247,
%T A353209 1153733,2696961,6268921,14502345,33410523,76691414,175465674,
%U A353209 400268753,910604494,2066396936,4678171694,10567687439,23822090548,53595047261,120353301562,269786130398,603734094052
%N A353209 Number of graph minors in the n-node wheel graph.
%C A353209 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
%H A353209 Andrew Howroyd, <a href="/A353209/b353209.txt">Table of n, a(n) for n = 1..1000</a>
%H A353209 Andrew Howroyd, <a href="/A353209/a353209.txt">Derivation of formula</a>, Jun 2025.
%H A353209 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphMinor.html">Graph Minor</a>.
%H A353209 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>.
%o A353209 (PARI) \\ DIK is unlabeled bracelet transform.
%o A353209 EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A353209 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}
%o A353209 seq(n)={ my(A=O(x*x^n),
%o A353209    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)),
%o A353209    gw = x*(DIK(x/(1 - x), n) - x*(1 + x)/(1 - x)),
%o A353209    gb = x^2*Ser(EulerT(Vec(x*(1 - x - x^2)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)) + A))));
%o A353209    Vec(((1 + gb - gc)/eta(x + A) + gw - 1)/(1 - x));
%o A353209 } \\ _Andrew Howroyd_, Jun 18 2025
%Y A353209 Cf. A353213.
%K A353209 nonn
%O A353209 1,2
%A A353209 _Eric W. Weisstein_, Apr 30 2022
%E A353209 a(12) from _Eric W. Weisstein_, Mar 15 2023
%E A353209 a(13)-a(18) from _Eric W. Weisstein_, Oct 11-20 2023
%E A353209 a(1)-a(3) prepended and a(19) onwards from _Andrew Howroyd_, Jun 18 2025