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

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

Offset

0,3

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.

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A243683 A323255 A167868 * A238751 A098672 A056210

Adjacent sequences: A368187 A368188 A368189 * A368191 A368192 A368193

Keyword

nonn

Author

Eric W. Weisstein, Dec 16 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

Status

approved