A353603 Number of graph minors in the n-pan graph.

0, 6, 15, 27, 46, 73, 115, 176, 268, 400, 594, 868, 1259, 1803, 2562, 3600, 5021, 6936, 9514, 12943, 17493, 23472, 31309, 41497, 54703, 71706, 93532, 121386, 156830, 201703, 258352, 329551, 418790, 530200, 668926, 841053, 1054090, 1316921, 1640414, 2037413

Offset

1,2

Comments

From Andrew Howroyd, Mar 01 2023: (Start)

The graph minors are any of the following:

- pan;

- cycle (maximum n vertices);

- cycle plus an isolated vertex;

- nonempty set of paths;

- claw plus a possibly empty set of paths.

In each of the above cases, at most n + 1 vertices may be used. The claw is a star with one branch that has length 1 and two others that may be longer. (End)

Extended to a(1) using the formula.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Graph Minor

Eric Weisstein's World of Mathematics, Pan Graph

Formula

a(n) = 3*(n-2) + A000070(n+1) - 1 + Sum_{j=0..n-3} floor((n-j-1)/2) * A000070(j). - Andrew Howroyd, Mar 01 2023

Mathematica

A000070[n_] := Sum[PartitionsP[k], {k, 0, n}]; Table[3 (n - 2) + A000070[n + 1] - 1 + Sum[Floor[(n - j - 1)/2] A000070[j], {j, 0, n - 3}], {n, 20}] (* Eric W. Weisstein, Oct 11 2023 *)

Prog

(PARI) seq(n)={my(v=vector(n+2), s=0); for(i=0, n+1, s+=numbpart(i); v[i+1]=s); vector(n-2, i, my(n=i+2); i*3 + v[n+2] - 1 + sum(j=0, n-3, (n-j-1)\2*v[1+j]))} \\ Andrew Howroyd, Mar 01 2023

Crossrefs

Cf. A000070.

Sequence in context: A255605 A171972 A225285 * A165454 A333646 A063525

Adjacent sequences: A353600 A353601 A353602 * A353604 A353605 A353606

Keyword

nonn

Author

Eric W. Weisstein, May 07 2022

Extensions

Terms a(21) and beyond from Andrew Howroyd, Mar 01 2023

Terms a(1)-a(2) prepended by Eric W. Weisstein, Oct 11 2023

Status

approved