A343994 Number of nodes in graph BC(n,2) when the internal nodes are counted with multiplicity.

3, 15, 58, 156, 339, 643, 1110, 1788, 2731, 3999, 5658, 7780, 10443, 13731, 17734, 22548, 28275, 35023, 42906, 52044, 62563, 74595, 88278, 103756, 121179, 140703, 162490, 186708, 213531, 243139, 275718, 311460, 350563, 393231, 439674, 490108, 544755, 603843, 667606, 736284, 810123

Offset

0,1

Comments

This graph BC(n,2) is also called SC(n,2) in earlier sequences (e.g. A331452). Once the Blomberg et al. paper is accepted for publication we will change the name from SC to BC.

Links

Table of n, a(n) for n=0..40.

Lars Blomberg, Scott R. Shannon, N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2020). Also arXiv:2009.07918. See Eq. (7.2).

Formula

a(n) = (n^4+10*n^3+25*n^2+12*n+12)/4.

Mathematica

Table[(n^4 + 10*n^3 + 25*n^2 + 12*n + 12)/4, {n, 0, 50}] (* Wesley Ivan Hurt, Sep 04 2022 *)

Crossrefs

Cf. A331452.

Sequence in context: A125673 A123007 A121695 * A017949 A263173 A049178

Adjacent sequences: A343991 A343992 A343993 * A343995 A343996 A343997

Keyword

nonn

Author

N. J. A. Sloane, May 20 2021

Status

approved