A185224 - OEIS

%I #30 Sep 08 2022 08:45:55

%S 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,

%T 99,114,139,160,194,224,268,310,370,426,504,582,687,790,927,1066,1247,

%U 1433,1667,1913,2222,2545,2944,3369,3888,4442,5112,5833,6697,7631,8739

%N Number of disconnected 2-regular simple graphs on n vertices with girth at least 4.

%C 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.

%H Andrew van den Hoeven, <a href="/A185224/b185224.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) = A008484(n) - A185114(n).

%o (Magma) A185224 := func<n|n eq 0 select 0 else #RestrictedPartitions(n,{4..n-1})>;

%Y 2-regular graphs with girth at least 4: A185114 (connected), this sequence (disconnected), A008484 (not necessarily connected).

%Y 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).

%Y 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).

%K nonn,easy

%O 0,11

%A _Jason Kimberley_, Feb 22 2011