A368190 Number of (undirected) cycles in the n-Dorogovtsev-Goltsev-Mendes graph.

0, 1, 11, 249, 74835, 5890739121, 34755832523270764251, 1207969003612007237832573159205646499369, 1459189113687796591938380205390010178829792070192521048490799792728844237848995

Offset: 0

Author

Eric W. Weisstein, Dec 16 2023

Keywords

• nonn

Comments

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

For n > 0, DGM(n) contains a unique longest cycle of length 3*2^(n-1).

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..11
• Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.
• Eric Weisstein's World of Mathematics, Graph Cycle.

Crossrefs

Cf. A007018, A368456, A367967 (5-cycles), A367968 (6-cycles).

Programs

PARI

a(n) = {my(t=0,b=1); for(k=1, n, t = 3*t + b^3; b += b^2); t} \\ Andrew Howroyd, Dec 30 2023

Formula

a(n) = 3*a(n-1) + A007018(n-1)^3 for n > 0. - Andrew Howroyd, Dec 30 2023

Extensions

Offset corrected and a(5) from Eric W. Weisstein, Dec 29 2023

Terms a(6) and beyond from Andrew Howroyd, Dec 30 2023