A185228 - OEIS

%I #16 Sep 08 2022 08:45:55

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,4,4,6,6,8,9,11,12,15,16,

%T 20,22,26,29,35,38,45,50,59,65,76,84,98,109,125,139,161,178,204,227,

%U 259,288,328,364,414,460,520,578,654,725,817,908,1021,1133

%N Number of disconnected 2-regular simple graphs on n vertices with girth at least 8.

%C Number of partitions of n with each part at least 8, and at least 2 parts.

%H Andrew Howroyd, <a href="/A185228/b185228.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) = A185328() - A185118(n). - _Andrew Howroyd_, Apr 18 2021

%o (Magma) A185228 := func<n|n eq 0 select 0 else #RestrictedPartitions(n,{8..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), A185227 (g=7), this sequence (g=8), A185229 (g=9).

%Y Cf. A185118, A185328.

%K nonn,easy

%O 0,19

%A _Jason Kimberley_, Feb 22 2011

%E Terms a(62) and beyond from _Andrew Howroyd_, Apr 18 2021