A184940 - OEIS

%I #29 Oct 18 2014 09:27:12

%S 1,1,2,5,1,16,0,57,2,263,2,1532,12,10747,31,87948,220,803885,1606,

%T 8020590,16828,86027734,193900,983417704,2452818,11913817317,32670329,

%U 1,152352034707,456028472,2,2050055948375,6636066091,8,28466137588780,100135577616,131

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

%C 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 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 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 1;

%e 1;

%e 2;

%e 5, 1;

%e 16, 0;

%e 57, 2;

%e 263, 2;

%e 1532, 12;

%e 10747, 31;

%e 87948, 220;

%e 803885, 1606;

%e 8020590, 16828;

%e 86027734, 193900;

%e 983417704, 2452818;

%e 11913817317, 32670329, 1;

%e 152352034707, 456028472, 2;

%e 2050055948375, 6636066091, 8;

%e 28466137588780, 100135577616, 131;

%Y 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 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 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 nonn,hard,tabf

%O 5,3

%A _Jason Kimberley_, Feb 24 2011