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A186715 Irregular triangle C(n,k)=number of connected k-regular 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,34

REFERENCES

M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley, Jan 29 2011]

LINKS

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

M. Meringer, Tables of Regular Graphs

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, 31478582, 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: A219486 A206499 A109527 * A219485 A057918 A242192

Adjacent sequences:  A186712 A186713 A186714 * A186716 A186717 A186718

KEYWORD

nonn,hard,tabf

AUTHOR

Jason Kimberley, Oct 17 2011

STATUS

approved

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Last modified October 21 23:13 EDT 2014. Contains 248381 sequences.