A343994 - OEIS

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

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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

Andrew Howroyd, Table of n, a(n) for n = 0..10000

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).

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

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

G.f.: (3 + 13*x^2 - 14*x^3 + 4*x^4)/(1 - x)^5. - Andrew Howroyd, Nov 11 2025

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