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%I #20 Sep 08 2022 08:45:55
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,4,5,6,7,9,10,12,14,17,19,23,
%T 26,31,35,41,47,55,62,72,82,95,107,124,140,161,182,208,235,269,303,
%U 345,389,442,497,564,634,718,806,910,1021,1152,1290,1452,1627,1828,2044,2294
%N Number of disconnected 2-regular simple graphs on n vertices with girth at least 7.
%C Number of partitions of n with each part at least 7, and at least 2 parts.
%H Andrew Howroyd, <a href="/A185227/b185227.txt">Table of n, a(n) for n = 0..1000</a>
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/D_k-reg_girth_ge_g_index">Index of sequences counting disconnected k-regular simple graphs with girth at least g</a>
%F a(n) = A185327() - A185117(n). - _Andrew Howroyd_, Apr 18 2021
%o (Magma) A185227 := func<n|n eq 0 select 0 else #RestrictedPartitions(n,{7..n-1})>;
%Y Disconnected 2-regular simple graphs with girth at least g: A165652 (g=3), A185224 (g=4), A185225 (g=5), A185226 (g=6), this sequence (g=7), A185228 (g=8), A185229 (g=9).
%Y Disconnected k-regular simple graphs with girth at least 7: A185217 (all k), A185207 (triangle); this sequence (k=2), A185237 (k=3).
%Y Cf. A185117, A185327.
%K nonn,easy
%O 0,17
%A _Jason Kimberley_, Feb 22 2011
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