A393909 Number of planar embedding isomorphism classes of the n-Dorogovtsev-Goltsev-Mendes graph.

1, 1, 2, 1228, 14089656148992, 50346839734076286938886836265405905350164480

Offset

0,3

Comments

These counts allow the mirror image as an isomorphism.

Using the indexing convention DGM(0) = P_2.

a(6) has 136 decimal digits and a(7) has 412 decimal digits. - Andrew Howroyd, Mar 03 2026

Links

Andrew Howroyd, Table of n, a(n) for n = 0..7

Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.

Eric Weisstein's World of Mathematics, Planar Embedding.

Formula

a(n) = (b(n)^3 + 2*b(n) + 3*c(n)*b(n))/12 for n >= 2, where b(n) = Product_{k=1..n} k^(3^(n-k)), c(n) = Product_{k=1..n} k^((3^(n-k)+1)/2). - Andrew Howroyd, Mar 03 2026

Prog

(PARI) a(n) = if(n<2, 1, my(b=prod(k=2, n, k^(3^(n-k))), c=prod(k=2, n, k^((3^(n-k)+1)/2))); (b^3 + 2*b + 3*c*b)/12) \\ Andrew Howroyd, Mar 03 2026

Crossrefs

Sequence in context: A281250 A369777 A171940 * A160003 A374793 A078170

Adjacent sequences: A393906 A393907 A393908 * A393910 A393911 A393912

Keyword

nonn

Author

Eric W. Weisstein, Mar 02 2026

Extensions

a(4) onward from Andrew Howroyd, Mar 03 2026

Status

approved