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A184941 Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth at least g.

%I A184941 #16 Oct 18 2014 09:25:05
%S A184941 1,1,2,6,1,16,0,59,2,265,2,1544,12,10778,31,88168,220,805491,1606,
%T A184941 8037418,16828,86221634,193900,985870522,2452818,11946487647,32670330,
%U A184941 1,152808063181,456028474,2,2056692014474,6636066099,8,28566273166527,100135577747,131
%N A184941 Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth at least g.
%C A184941 The first column is for girth at least 3. The row length sequence starts: 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4. The row length is incremented to g-2 when n reaches A037233(g).
%H A184941 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_ge_g_index">Index of sequences counting connected k-regular simple graphs with girth at least g</a>
%e A184941 1;
%e A184941 1;
%e A184941 2;
%e A184941 6, 1;
%e A184941 16, 0;
%e A184941 59, 2;
%e A184941 265, 2;
%e A184941 1544, 12;
%e A184941 10778, 31;
%e A184941 88168, 220;
%e A184941 805491, 1606;
%e A184941 8037418, 16828;
%e A184941 86221634, 193900;
%e A184941 985870522, 2452818;
%e A184941 11946487647, 32670330, 1;
%e A184941 152808063181, 456028474, 2;
%e A184941 2056692014474, 6636066099, 8;
%e A184941 28566273166527, 100135577747, 131;
%Y A184941 Connected 4-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).
%Y A184941 Connected 4-regular simple graphs with girth exactly g: A184940 (triangle); chosen g: A184943 (g=3), A184944 (g=4), A184945 (g=5), A184946 (g=6).
%Y A184941 Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), this sequence (k=4), A184951 (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8).
%K A184941 nonn,hard,tabf
%O A184941 5,3
%A A184941 _Jason Kimberley_, Jan 10 2012