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A185225 Number of disconnected 2-regular simple graphs on n vertices with girth at least 5. 9
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 14, 17, 20, 25, 29, 35, 41, 49, 57, 69, 79, 94, 109, 128, 149, 175, 201, 235, 271, 316, 363, 422, 483, 559, 642, 739, 846, 974, 1111, 1276, 1455, 1665, 1896, 2167, 2463, 2808, 3188, 3626, 4111, 4672, 5286, 5994, 6777, 7670, 8661, 9790, 11036 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Number of partitions of n with smallest part >= 5 and at least 2 parts.

LINKS

Table of n, a(n) for n=0..67.

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

FORMULA

G.f.: -1/(1-q) + sum(n>=0, q^n/prod(k=5..n, 1-q^k ) ).  [Joerg Arndt, Jul 26 2011]

PROG

(PARI) N=66;  q='q+O('q^N);

gf= -1/(1-q) + sum(n=0, N, q^n/prod(k=5, n, 1-q^k) ) /* = +q^10 +q^11 +2*q^12 +... */

v=Vec(gf+'a); v[1]=0; v /* Joerg Arndt, Jul 26 2011 */

(MAGMA) A185225 := func<n|n eq 0 select 0 else #RestrictedPartitions(n, {5..n-1})>;

CROSSREFS

Disconnected 2-regular simple graphs with girth at least g: A165652 (g=3), A185224 (g=4), this sequence (g=5), A185226 (g=6), A185227 (g=7), A185228 (g=8), A185229 (g=9).

Sequence in context: A114096 A008582 A069911 * A027196 A325877 A100928

Adjacent sequences:  A185222 A185223 A185224 * A185226 A185227 A185228

KEYWORD

nonn,easy

AUTHOR

Jason Kimberley, Feb 22 2011

EXTENSIONS

Added more terms, Joerg Arndt, Jul 26 2011.

STATUS

approved

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Last modified August 4 08:55 EDT 2021. Contains 346445 sequences. (Running on oeis4.)