cp's OEIS Frontend

A186714 Triangular array C(n, k) = number of connected k-regular graphs, having girth at least 4, with n nodes, 0 <= k <= n div 2.

%I A186714 #46 Jul 09 2025 04:32:59
%S A186714 1,0,1,0,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0,1,2,1,0,0,1,0,0,0,0,1,6,2,
%T A186714 1,0,0,1,0,2,0,0,0,1,22,12,1,1,0,0,1,0,31,0,0,0,0,1,110,220,7,1,1,0,0,
%U A186714 1,0,1606,0,1,0,0,0,1,792,16828,388,9,1,1,0,0,1,0,193900,0,6,0,0,0,0,1
%N A186714 Triangular array C(n, k) = number of connected k-regular graphs, having girth at least 4, with n nodes, 0 <= k <= n div 2.
%H A186714 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_4">Connected regular graphs with girth at least 4</a>
%H A186714 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 A186714 01: 1;
%e A186714 02: 0,1;
%e A186714 03: 0,0;
%e A186714 04: 0,0,1;
%e A186714 05: 0,0,1;
%e A186714 06: 0,0,1,1;
%e A186714 07: 0,0,1,0;
%e A186714 08: 0,0,1,2,1;
%e A186714 09: 0,0,1,0,0;
%e A186714 10: 0,0,1,6,2,1;
%e A186714 11: 0,0,1,0,2,0;
%e A186714 12: 0,0,1,22,12,1,1;
%e A186714 13: 0,0,1,0,31,0,0;
%e A186714 14: 0,0,1,110,220,7,1,1;
%e A186714 15: 0,0,1,0,1606,0,1,0;
%e A186714 16: 0,0,1,792,16828,388,9,1,1;
%e A186714 17: 0,0,1,0,193900,0,6,0,0;
%e A186714 18: 0,0,1,7805,2452818,406824,267,8,1,1;
%e A186714 19: 0,0,1,0,32670330,0,3727,0,0,0;
%e A186714 20: 0,0,1,97546,456028474,1125022325,483012,741,13,1,1;
%e A186714 21: 0,0,1,0,6636066099,0,69823723,0,1,0,0;
%e A186714 22: 0,0,1,1435720,100135577747,3813549359274,14836130862,2887493,?,14,1,1;
%e A186714 23: 0,0,1,0,1582718912968,0,?,0,?,0,0;
%Y A186714 The sum of the n-th row is A186724(n).
%Y A186714 Connected k-regular simple graphs with girth at least 4: A186724 (any k), this sequence (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).
%Y A186714 Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *at least* g: A068934 (g=3), this sequence (g=4), A186715 (g=5), A186716 (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).
%Y A186714 Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *exactly* g: A186733 (g=3), A186734 (g=4).
%K A186714 nonn,tabf,hard
%O A186714 1,23
%A A186714 _Jason Kimberley_, Sep 04 2011