A185226 Number of disconnected 2-regular simple graphs on n vertices with girth at least 6.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 5, 5, 7, 8, 10, 11, 15, 16, 20, 23, 28, 31, 39, 43, 52, 59, 70, 79, 95, 106, 125, 142, 166, 187, 220, 247, 287, 325, 375, 423, 490, 551, 633, 715, 818, 921, 1055, 1186, 1352, 1522, 1729, 1943, 2208

Offset

0,15

Comments

Number of partitions of n with each part at least 6, and at least 2 parts.

Links

Table of n, a(n) for n=0..60.

Jason Kimberley, Disconnected regular graphs with girth at least 6

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

Formula

a(n) = A185326(n) - A185116(n).

Prog

(Magma) A185226 := func<n|n eq 0 select 0 else #RestrictedPartitions(n, {6..n-1})>;

Crossrefs

Disconnected k-regular simple graphs with girth at least 6: A185216 (all k), A185206 (triangle); this sequence (k=2), A185236 (k=3), A185246 (k=4).

Disconnected 2-regular simple graphs with girth at least g: A165652 (g=3), A185224 (g=4), A185225 (g=5), this sequence (g=6), A185227 (g=7), A185228 (g=8), A185229 (g=9).

Sequence in context: A239513 A029018 A238217 * A096765 A025147 A364613

Adjacent sequences: A185223 A185224 A185225 * A185227 A185228 A185229

Keyword

nonn,easy

Author

Jason Kimberley, Feb 22 2011

Status

approved