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A185644 Triangular array E(n,k) counting, not necessarily connected, k-regular simple graphs on n vertices with girth exactly 4. 6
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 5, 2, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 21, 12, 1, 1, 0, 0, 2, 0, 31, 0, 0, 0, 0, 3, 103, 220, 7, 1, 1, 0, 0, 3, 0, 1606, 0, 1, 0, 0, 0, 5, 752, 16829, 388, 9, 1, 1, 0, 0, 5, 0, 193900, 0, 6, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,23

COMMENTS

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

LINKS

Jason Kimberley, Table of n, a(i)=E(n,k) for i = 1..139 (n = 1..22)

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

FORMULA

E(n,k) = A186734(n,k) + A210704(n,k), noting the differing row lengths.

E(n,k) = A185304(n,k) - A185305(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, 1, 2, 1;

09: 0, 0, 1, 0, 0;

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

11: 0, 0, 1, 0, 2, 0;

12: 0, 0, 2, 21, 12, 1, 1;

13: 0, 0, 2, 0, 31, 0, 0;

14: 0, 0, 3, 103, 220, 7, 1, 1;

15: 0, 0, 3, 0, 1606, 0, 1, 0;

16: 0, 0, 5, 752, 16829, 388, 9, 1, 1;

17: 0, 0, 5, 0, 193900, 0, 6, 0, 0;

18: 0, 0, 7, 7385, 2452820, 406824, 267, 8, 1, 1;

19: 0, 0, 8, 0, 32670331, 0, 3727, 0, 0, 0;

20: 0, 0, 11, 91939, 456028487, 1125022326, 483012, 741, 13, 1, 1;

21: 0, 0, 12, 0, 6636066126, 0, 69823723, 0, 1, 0, 0;

22: 0, 0, 16, 1345933, 100135577863, 3813549359275, 14836130862, 2887493, ?, 14, 1;

CROSSREFS

The sum of the n-th row of this sequence is A198314(n).

Not necessarily connected k-regular simple graphs girth exactly 4: A198314 (any k), this sequence (triangle); fixed k: A026797 (k=2), A185134 (k=3), A185144 (k=4).

Sequence in context: A116905 A115079 A286562 * A319080 A025435 A304685

Adjacent sequences:  A185641 A185642 A185643 * A185645 A185646 A185647

KEYWORD

nonn,hard,tabf

AUTHOR

Jason Kimberley, Feb 22 2013

STATUS

approved

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Last modified February 20 15:52 EST 2020. Contains 332078 sequences. (Running on oeis4.)