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URL: https://oeis.org/A186734

⇱ A186734 - OEIS

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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
OFFSET
1,23
COMMENTS
In the n-th row 0 <= 2k <= n.
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
KEYWORD
nonn,hard,tabf
AUTHOR
Jason Kimberley, Mar 20 2013
STATUS
approved