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A186734 Triangular array C(n,k) counting connected k-regular simple graphs on n vertices with girth exactly 4.

%I A186734 #12 Aug 30 2013 11:32:08
%S A186734 0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,5,2,
%T A186734 1,0,0,0,0,2,0,0,0,0,20,12,1,1,0,0,0,0,31,0,0,0,0,0,101,220,7,1,1,0,0,
%U A186734 0,0,1606,0,1,0,0,0,0,743,16828,388,9,1,1,0,0,0,0,193900,0,6,0,0,0,0,0,7350
%N A186734 Triangular array C(n,k) counting connected k-regular simple graphs on n vertices with girth exactly 4.
%C A186734 In the n-th row 0 <= 2k <= n.
%H A186734 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>
%F A186734 C(n,k) = A186714(n,k) - A186715(n,k), noting the differing row lengths.
%F A186734 E(n,k) = A185644(n,k) - A210704(n,k), noting the differing row lengths.
%e A186734 01: 0;
%e A186734 02: 0, 0;
%e A186734 03: 0, 0;
%e A186734 04: 0, 0, 1;
%e A186734 05: 0, 0, 0;
%e A186734 06: 0, 0, 0, 1;
%e A186734 07: 0, 0, 0, 0;
%e A186734 08: 0, 0, 0, 2, 1;
%e A186734 09: 0, 0, 0, 0, 0;
%e A186734 10: 0, 0, 0, 5, 2, 1;
%e A186734 11: 0, 0, 0, 0, 2, 0;
%e A186734 12: 0, 0, 0, 20, 12, 1, 1;
%e A186734 13: 0, 0, 0, 0, 31, 0, 0;
%e A186734 14: 0, 0, 0, 101, 220, 7, 1, 1;
%e A186734 15: 0, 0, 0, 0, 1606, 0, 1, 0;
%e A186734 16: 0, 0, 0, 743, 16828, 388, 9, 1, 1;
%e A186734 17: 0, 0, 0, 0, 193900, 0, 6, 0, 0;
%e A186734 18: 0, 0, 0, 7350, 2452818, 406824, 267, 8, 1, 1;
%e A186734 19: 0, 0, 0, 0, 32670329, 0, 3727, 0, 0, 0;
%e A186734 20: 0, 0, 0, 91763, 456028472, 1125022325, 483012, 741, 13, 1, 1;
%e A186734 21: 0, 0, 0, 0, 6636066091, 0, 69823723, 0, 1, 0, 0;
%Y A186734 The sum of the n-th row of this sequence is A186744(n).
%Y A186734 Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *exactly* g: A186733 (g=3), this sequence (g=4).
%Y A186734 Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *at least* g: A068934 (g=3), A186714 (g=4).
%K A186734 nonn,hard,tabf
%O A186734 1,23
%A A186734 _Jason Kimberley_, Mar 20 2013