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A185224
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Number of disconnected 2-regular simple graphs on n vertices with girth at least 4.
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18
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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
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OFFSET
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0,11
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COMMENTS
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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.
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LINKS
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FORMULA
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PROG
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(Magma) A185224 := func<n|n eq 0 select 0 else #RestrictedPartitions(n, {4..n-1})>;
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CROSSREFS
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2-regular graphs with girth at least 4: A185114 (connected), this sequence (disconnected), A008484 (not necessarily connected).
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).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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