

A186715


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


15



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
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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) 137146. [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 kregular 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 kregular 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 kregular 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 kregular graphs on n vertices with girth exactly g: A186733 (g=3), A186734 (g=4).
Sequence in context: A206499 A277885 A109527 * A219485 A057918 A242192
Adjacent sequences: A186712 A186713 A186714 * A186716 A186717 A186718


KEYWORD

nonn,hard,tabf


AUTHOR

Jason Kimberley, Oct 17 2011


STATUS

approved



