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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

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

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: 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 23 15:24 EST 2020. Contains 332167 sequences. (Running on oeis4.)