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A185227
Number of disconnected 2-regular simple graphs on n vertices with girth at least 7.
12
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.
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).
Sequence in context: A114372 A046676 A003114 * A217569 A335766 A026823
KEYWORD
nonn,easy
AUTHOR
Jason Kimberley, Feb 22 2011
STATUS
approved