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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; 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: A161254 A241313 A241317 * A001996 A317084 A122134 Adjacent sequences:  A185221 A185222 A185223 * A185225 A185226 A185227 KEYWORD nonn,easy AUTHOR Jason Kimberley, Feb 22 2011 STATUS approved

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Last modified February 20 14:14 EST 2020. Contains 332078 sequences. (Running on oeis4.)