login
Irregular triangle C(n,g) counting the connected 5-regular simple graphs on 2n vertices with girth at least g.
7

%I #19 May 01 2014 02:40:01

%S 1,3,60,1,7848,1,3459383,7,2585136675,388,2807105250897,406824

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

%C The first column is for girth at least 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_ge_g_index">Index of sequences counting connected k-regular simple graphs with girth at least g</a>

%e 1;

%e 3;

%e 60, 1;

%e 7848, 1;

%e 3459383, 7;

%e 2585136675, 388;

%e 2807105250897, 406824;

%Y Connected 5-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006821 (g=3), A058275 (g=4), A205295 (g=5).

%Y Connected 5-regular simple graphs with girth exactly g: A184950 (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 at least g: A185131 (k=3), A184941 (k=4), this sequence (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8).

%K nonn,hard,more,tabf

%O 3,2

%A _Jason Kimberley_, Jan 10 2012

%E a(14) from _Jason Kimberley_, Dec 26 2012