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A186734 Triangular array C(n,k) counting connected k-regular simple graphs on n vertices with girth exactly 4. 9
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,23

COMMENTS

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

LINKS

Table of n, a(n) for n=1..93.

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

FORMULA

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

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

EXAMPLE

01: 0;

02: 0, 0;

03: 0, 0;

04: 0, 0, 1;

05: 0, 0, 0;

06: 0, 0, 0, 1;

07: 0, 0, 0, 0;

08: 0, 0, 0, 2, 1;

09: 0, 0, 0, 0, 0;

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

11: 0, 0, 0, 0, 2, 0;

12: 0, 0, 0, 20, 12, 1, 1;

13: 0, 0, 0, 0, 31, 0, 0;

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

15: 0, 0, 0, 0, 1606, 0, 1, 0;

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

17: 0, 0, 0, 0, 193900, 0, 6, 0, 0;

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

19: 0, 0, 0, 0, 32670329, 0, 3727, 0, 0, 0;

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

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

CROSSREFS

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

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).

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).

Sequence in context: A037860 A037878 A107652 * A196096 A249344 A067150

Adjacent sequences:  A186731 A186732 A186733 * A186735 A186736 A186737

KEYWORD

nonn,hard,tabf

AUTHOR

Jason Kimberley, Mar 20 2013

STATUS

approved

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Last modified February 19 10:24 EST 2019. Contains 320310 sequences. (Running on oeis4.)