A397743 Number of assembly trees for the n-sunlet graph.

1, 5, 90, 2210, 67800, 2484750, 105772800, 5128126100, 278995708800, 16834806218750, 1115967716160000, 80627283335101500, 6306411043525632000, 530946503562997987500, 47876129916092928000000, 4603521212261405490225000, 470209485165582143631360000, 50843713447609660550744718750

Offset

1,2

Comments

The n-sunlet graph is properly defined for n >= 3. For n = 1 and 2 a loop or double edge with pendent vertices is used.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Assembly Number.

Eric Weisstein's World of Mathematics, Sunlet Graph.

Formula

a(n) = n*A062980(n-1)/2 for n > 1.

Prog

(PARI) seq(n) = { my(v=vector(n)); v[1] = 2; v[2] = 5; for(n=3, n, v[n] = 6*(n-1)*v[n-1] + sum(k=2, n-2, v[k]*v[n-k])); vector(#v, n, v[n]*n)/2 }

Crossrefs

Cf. A062980 (for centipede graph).

Sequence in context: A301359 A352590 A037297 * A277303 A361551 A323570

Adjacent sequences: A397737 A397738 A397741 * A397744 A397745 A397746

Keyword

nonn,new

Author

Andrew Howroyd, Jul 08 2026

Status

approved