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A185224
Number of disconnected 2-regular simple graphs on n vertices with girth at least 4.
18
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 15, 17, 23, 26, 33, 38, 49, 56, 69, 80, 99, 114, 139, 160, 194, 224, 268, 310, 370, 426, 504, 582, 687, 790, 927, 1066, 1247, 1433, 1667, 1913, 2222, 2545, 2944, 3369, 3888, 4442, 5112, 5833, 6697, 7631, 8739
OFFSET
0,11
COMMENTS
a(n) is also the number of partitions of n with each part at least 4 and at most n-1. The integer i corresponds to the i-cycle; addition of integers corresponds to disconnected union of cycles.
FORMULA
a(n) = A008484(n) - A185114(n).
PROG
(Magma) A185224 := func<n|n eq 0 select 0 else #RestrictedPartitions(n, {4..n-1})>;
CROSSREFS
2-regular graphs with girth at least 4: A185114 (connected), this sequence (disconnected), A008484 (not necessarily connected).
Disconnected k-regular simple graphs with girth at least 4: A185214 (any k), A185204 (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).
Disconnected 2-regular simple graphs with girth at least g [partitions of n with each part i being g <= i < n]: A165652 (g=3), this sequence (g=4), A185225 (g=5), A185226 (g=6), A185227 (g=7), A185228 (g=8), A185229 (g=9).
Sequence in context: A241313 A241317 A357456 * A001996 A317084 A122134
KEYWORD
nonn,easy
AUTHOR
Jason Kimberley, Feb 22 2011
STATUS
approved