A186715 Irregular triangle C(n,k)=number of connected k-regular graphs on n vertices having girth at least five.

1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 9, 0, 0, 1, 0, 0, 0, 1, 49, 0, 0, 1, 0, 0, 0, 1, 455, 0, 0, 1, 0, 1, 0, 0, 1, 5783, 2, 0, 0, 1, 0, 8, 0, 0, 1, 90938, 131, 0, 0, 1, 0, 3917, 0, 0, 1, 1620479, 123859

Offset

1,34

Comments

Brendan McKay has observed that C(26,3) = 31478584 is output by genreg, minibaum, and snarkhunter, but Meringer's table currently has C(26,3) = 31478582. - Jason Kimberley, May 19 2017

Links

Jason Kimberley, Table of i, a(i) for i = 1..111 (n = 1..28)

M. Meringer, Tables of Regular Graphs

M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. [Jason Kimberley, Jan 29 2011]

Jason Kimberley, Partial table of i, a(i) for i = 1..137 (n = 1..33)

Jason Kimberley, Partial table of i, n, k, a(i)=C(n,k) for n = 1..33

Jason Kimberley, Connected regular graphs with girth at least 5

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Example

01: 1;
02: 0, 1;
03: 0, 0;
04: 0, 0;
05: 0, 0, 1;
06: 0, 0, 1;
07: 0, 0, 1;
08: 0, 0, 1;
09: 0, 0, 1;
10: 0, 0, 1, 1;
11: 0, 0, 1, 0;
12: 0, 0, 1, 2;
13: 0, 0, 1, 0;
14: 0, 0, 1, 9;
15: 0, 0, 1, 0;
16: 0, 0, 1, 49;
17: 0, 0, 1, 0;
18: 0, 0, 1, 455;
19: 0, 0, 1, 0, 1;
20: 0, 0, 1, 5783, 2;
21: 0, 0, 1, 0, 8;
22: 0, 0, 1, 90938, 131;
23: 0, 0, 1, 0, 3917;
24: 0, 0, 1, 1620479, 123859;
25: 0, 0, 1, 0, 4131991;
26: 0, 0, 1, 31478584, 132160608;
27: 0, 0, 1, 0, 4018022149;
28: 0, 0, 1, 656783890, 118369811960;

Crossrefs

The row sums are given by A186725.

Connected k-regular simple graphs with girth at least 5: A186725 (all k), this sequence (triangle); A185115 (k=2), A014372 (k=3), A058343 (k=4), A205295 (k=5).

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), this sequence (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: A186733 (g=3), A186734 (g=4).

Sequence in context: A109527 A373241 A362424 * A331983 A219485 A337165

Adjacent sequences: A186712 A186713 A186714 * A186716 A186717 A186718

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Oct 17 2011

Status

approved