A368456 Number of independent vertex sets in the n-Dorogovtsev-Goltsev-Mendes graph.

3, 4, 14, 1120, 1129856000, 1429646991180169216000000000, 2922003679260403682236915960536301659966658013592289280000000000000000000000000000

Offset: 0

Author

Eric W. Weisstein, Dec 25 2023

Keywords

• nonn

Comments

Using the indexing convention that DGM(0) = P_2.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..8
• Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.
• Eric Weisstein's World of Mathematics, Independent Vertex Set.

Programs

PARI

a(n) = {my(b=1, c=1); for(k=1, n, c = b*c^2; b = b^3 + c); b + 2*c} \\ Andrew Howroyd, Dec 30 2023

Formula

a(n) = b(n) + 2*c(n) where b(0) = c(0) = 1 and c(n) = b(n-1)*c(n-1)^2, b(n) = c(n) + b(n-1)^3 for n > 0. - Andrew Howroyd, Dec 30 2023

Extensions

a(0) prepended and terms a(5) and beyond from Andrew Howroyd, Dec 30 2023