%I #21 Sep 08 2022 08:45:55

%S 0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,5,5,7,8,10,11,15,16,20,23,28,31,

%T 39,43,52,59,70,79,95,106,125,142,166,187,220,247,287,325,375,423,490,

%U 551,633,715,818,921,1055,1186,1352,1522,1729,1943,2208

%N Number of disconnected 2-regular simple graphs on n vertices with girth at least 6.

%C Number of partitions of n with each part at least 6, and at least 2 parts.

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/D_girth_ge_6">Disconnected regular graphs with girth at least 6</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) = A185326(n) - A185116(n).

%o (Magma) A185226 := func<n|n eq 0 select 0 else #RestrictedPartitions(n,{6..n-1})>;

%Y Disconnected k-regular simple graphs with girth at least 6: A185216 (all k), A185206 (triangle); this sequence (k=2), A185236 (k=3), A185246 (k=4).

%Y Disconnected 2-regular simple graphs with girth at least g: A165652 (g=3), A185224 (g=4), A185225 (g=5), this sequence (g=6), A185227 (g=7), A185228 (g=8), A185229 (g=9).

%K nonn,easy

%O 0,15

%A _Jason Kimberley_, Feb 22 2011