A185228 Number of disconnected 2-regular simple graphs on n vertices with girth at least 8.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 9, 11, 12, 15, 16, 20, 22, 26, 29, 35, 38, 45, 50, 59, 65, 76, 84, 98, 109, 125, 139, 161, 178, 204, 227, 259, 288, 328, 364, 414, 460, 520, 578, 654, 725, 817, 908, 1021, 1133

Offset

0,19

Comments

Number of partitions of n with each part at least 8, and at least 2 parts.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Formula

a(n) = A185328() - A185118(n). - Andrew Howroyd, Apr 18 2021

Prog

(Magma) A185228 := func<n|n eq 0 select 0 else #RestrictedPartitions(n, {8..n-1})>;

Crossrefs

Disconnected 2-regular simple graphs with girth at least g: A165652 (g=3), A185224 (g=4), A185225 (g=5), A185226 (g=6), A185227 (g=7), this sequence (g=8), A185229 (g=9).

Cf. A185118, A185328.

Sequence in context: A050365 A029026 A003106 * A026824 A025149 A026799

Adjacent sequences: A185225 A185226 A185227 * A185229 A185230 A185231

Keyword

nonn,easy

Author

Jason Kimberley, Feb 22 2011

Extensions

Terms a(62) and beyond from Andrew Howroyd, Apr 18 2021

Status

approved