A185227 Number of disconnected 2-regular simple graphs on n vertices with girth at least 7.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 31, 35, 41, 47, 55, 62, 72, 82, 95, 107, 124, 140, 161, 182, 208, 235, 269, 303, 345, 389, 442, 497, 564, 634, 718, 806, 910, 1021, 1152, 1290, 1452, 1627, 1828, 2044, 2294

Offset

0,17

Comments

Number of partitions of n with each part at least 7, 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) = A185327() - A185117(n). - Andrew Howroyd, Apr 18 2021

Prog

(Magma) A185227 := func<n|n eq 0 select 0 else #RestrictedPartitions(n, {7..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), this sequence (g=7), A185228 (g=8), A185229 (g=9).

Disconnected k-regular simple graphs with girth at least 7: A185217 (all k), A185207 (triangle); this sequence (k=2), A185237 (k=3).

Cf. A185117, A185327.

Sequence in context: A114372 A046676 A003114 * A217569 A335766 A026823

Adjacent sequences: A185224 A185225 A185226 * A185228 A185229 A185230

Keyword

nonn,easy

Author

Jason Kimberley, Feb 22 2011

Status

approved