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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 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
Andrew van den Hoeven, Table of n, a(n) for n = 0..1000
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

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)