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A184940 Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth exactly g.

%I A184940 #29 Oct 18 2014 09:27:12
%S A184940 1,1,2,5,1,16,0,57,2,263,2,1532,12,10747,31,87948,220,803885,1606,
%T A184940 8020590,16828,86027734,193900,983417704,2452818,11913817317,32670329,
%U A184940 1,152352034707,456028472,2,2050055948375,6636066091,8,28466137588780,100135577616,131
%N A184940 Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth exactly g.
%C A184940 The first column is for girth exactly 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 A184940 Jason Kimberley, <a href="/A184940/a184940.txt">Incomplete table of i, n, g, C(n,g)=a(i) for row n = 5..36</a>
%H A184940 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>
%e A184940 1;
%e A184940 1;
%e A184940 2;
%e A184940 5, 1;
%e A184940 16, 0;
%e A184940 57, 2;
%e A184940 263, 2;
%e A184940 1532, 12;
%e A184940 10747, 31;
%e A184940 87948, 220;
%e A184940 803885, 1606;
%e A184940 8020590, 16828;
%e A184940 86027734, 193900;
%e A184940 983417704, 2452818;
%e A184940 11913817317, 32670329, 1;
%e A184940 152352034707, 456028472, 2;
%e A184940 2050055948375, 6636066091, 8;
%e A184940 28466137588780, 100135577616, 131;
%Y A184940 Connected 4-regular simple graphs with girth at least g: A184941 (triangle); chosen g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).
%Y A184940 Connected 4-regular simple graphs with girth exactly g: this sequence (triangle); chosen g: A184943 (g=3), A184944 (g=4), A184945 (g=5), A184946 (g=6).
%Y A184940 Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth exactly g: A198303 (k=3), this sequence (k=4), A184950 (k=5), A184960 (k=6), A184970 (k=7), A184980 (k=8).
%K A184940 nonn,hard,tabf
%O A184940 5,3
%A A184940 _Jason Kimberley_, Feb 24 2011