A184950 - OEIS

%I #15 May 01 2014 02:37:01

%S 1,3,59,1,7847,1,3459376,7,2585136287,388,2807104844073,406824

%N Irregular triangle C(n,g) counting the connected 5-regular simple graphs on 2n vertices with girth exactly g.

%C The first column is for girth exactly 3. The row length sequence starts: 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4. The row length is incremented to g-2 when 2n reaches A054760(5,g).

%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>

%H Jason Kimberley, <a href="/A184950/a184950.txt">Incomplete table of i, n, g, C(n,g)=a(i) for row n = 3..22</a>

%e 1;

%e 3;

%e 59, 1;

%e 7847, 1;

%e 3459376, 7;

%e 2585136287, 388;

%e 2807104844073, 406824;

%e ?, 1125022325;

%e ?, 3813549359274;

%Y Connected 5-regular simple graphs with girth at least g: A184951 (triangle); chosen g: A006821 (g=3), A058275 (g=4).

%Y Connected 5-regular simple graphs with girth exactly g: this sequence (triangle); chosen g: A184953 (g=3), A184954 (g=4), A184955 (g=5).

%Y Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth exactly g: A198303 (k=3), A184940 (k=4), this sequence (k=5), A184960 (k=6), A184970 (k=7), A184980 (k=8).

%K nonn,hard,more,tabf

%O 3,2

%A _Jason Kimberley_, Feb 24 2011