A186734 - OEIS

%I #12 Aug 30 2013 11:32:08

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

%C In the n-th row 0 <= 2k <= n.

%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>

%F C(n,k) = A186714(n,k) - A186715(n,k), noting the differing row lengths.

%F E(n,k) = A185644(n,k) - A210704(n,k), noting the differing row lengths.

%e 01: 0;

%e 02: 0, 0;

%e 03: 0, 0;

%e 04: 0, 0, 1;

%e 05: 0, 0, 0;

%e 06: 0, 0, 0, 1;

%e 07: 0, 0, 0, 0;

%e 08: 0, 0, 0, 2, 1;

%e 09: 0, 0, 0, 0, 0;

%e 10: 0, 0, 0, 5, 2, 1;

%e 11: 0, 0, 0, 0, 2, 0;

%e 12: 0, 0, 0, 20, 12, 1, 1;

%e 13: 0, 0, 0, 0, 31, 0, 0;

%e 14: 0, 0, 0, 101, 220, 7, 1, 1;

%e 15: 0, 0, 0, 0, 1606, 0, 1, 0;

%e 16: 0, 0, 0, 743, 16828, 388, 9, 1, 1;

%e 17: 0, 0, 0, 0, 193900, 0, 6, 0, 0;

%e 18: 0, 0, 0, 7350, 2452818, 406824, 267, 8, 1, 1;

%e 19: 0, 0, 0, 0, 32670329, 0, 3727, 0, 0, 0;

%e 20: 0, 0, 0, 91763, 456028472, 1125022325, 483012, 741, 13, 1, 1;

%e 21: 0, 0, 0, 0, 6636066091, 0, 69823723, 0, 1, 0, 0;

%Y The sum of the n-th row of this sequence is A186744(n).

%Y 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 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 nonn,hard,tabf

%O 1,23

%A _Jason Kimberley_, Mar 20 2013