A186733 Triangular array C(n,r) = number of connected r-regular graphs, having girth exactly 3, with n nodes, for 0 <= r < n.
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 3, 5, 3, 1, 1, 0, 0, 0, 0, 16, 0, 4, 0, 1, 0, 0, 0, 13, 57, 59, 21, 5, 1, 1, 0, 0, 0, 0, 263, 0, 266, 0, 6, 0, 1, 0, 0, 0, 63, 1532, 7847, 7848, 1547, 94, 9, 1, 1, 0, 0, 0, 0, 10747, 0, 367860, 0, 10786
Offset: 1
Examples
01: 0 ; 02: 0, 0 ; 03: 0, 0, 1 ; 04: 0, 0, 0, 1 ; 05: 0, 0, 0, 0, 1 ; 06: 0, 0, 0, 1, 1, 1 ; 07: 0, 0, 0, 0, 2, 0, 1 ; 08: 0, 0, 0, 3, 5, 3, 1, 1 ; 09: 0, 0, 0, 0, 16, 0, 4, 0, 1 ; 10: 0, 0, 0, 13, 57, 59, 21, 5, 1, 1 ; 11: 0, 0, 0, 0, 263, 0, 266, 0, 6, 0, 1 ; 12: 0, 0, 0, 63, 1532, 7847, 7848, 1547, 94, 9, 1, 1 ; 13: 0, 0, 0, 0, 10747, 0, 367860, 0, 10786, 0, 10, 0, 1 ; 14: 0, 0, 0, 399, 87948, 3459376, 21609299, 21609300, 3459386, 88193, 540, 13, 1, 1 ; 15: 0, 0, 0, 0, 803885, 0, 1470293674, 0, 1470293676, 0, 805579, 0, 17, 0, 1 ; 16: 0, 0, 0, 3268, 8020590, 2585136287, 113314233799, 733351105933, 733351105934, 113314233813, 2585136741, 8037796, 4207, 21, 1, 1;
Links
- Jason Kimberley, Table of i, a(i)=C(n,r) for i = 1..136 (n = 1..16)
- Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g
Crossrefs
The sum of the n-th row is A186743(n).
Connected k-regular simple graphs with girth exactly 3: this sequence (triangle), A186743 (any k); chosen k: A006923 (k=3), A184943 (k=4), A184953 (k=5), A184963 (k=6), A184973 (k=7), A184983 (k=8), A184993 (k=9).
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), A186715 (g=5), A186716 (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).
Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *exactly* g: this sequence (g=3), A186734 (g=4).