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A185304
Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 4.
10
1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 2, 1, 1, 0, 2, 0, 0, 1, 1, 3, 6, 2, 1, 1, 0, 3, 0, 2, 0, 1, 1, 5, 23, 12, 1, 1, 1, 0, 5, 0, 31, 0, 0, 1, 1, 7, 112, 220, 7, 1, 1, 1, 0, 8, 0, 1606, 0, 1, 0, 1, 1, 11, 801, 16829, 388, 9, 1, 1, 1, 0, 12, 0, 193900, 0, 6, 0, 0, 1, 1, 16, 7840, 2452820, 406824, 267, 8, 1, 1, 1, 0, 18, 0, 32670332, 0, 3727, 0, 0, 0
OFFSET
1,22
COMMENTS
Row sums give A185314.
FORMULA
E(n,k) = A186714(n,k) + A185204(n,k).
EXAMPLE
1: 1;
2: 1, 1;
3: 1, 0;
4: 1, 1, 1;
5: 1, 0, 1;
6: 1, 1, 1, 1;
7: 1, 0, 1, 0;
8: 1, 1, 2, 2, 1;
9: 1, 0, 2, 0, 0;
10: 1, 1, 3, 6, 2, 1;
11: 1, 0, 3, 0, 2, 0;
12: 1, 1, 5, 23, 12, 1, 1;
13: 1, 0, 5, 0, 31, 0, 0;
14: 1, 1, 7, 112, 220, 7, 1, 1;
15: 1, 0, 8, 0, 1606, 0, 1, 0;
16: 1, 1, 11, 801, 16829, 388, 9, 1, 1;
17: 1, 0, 12, 0, 193900, 0, 6, 0,0;
18: 1, 1, 16, 7840, 2452820, 406824, 267, 8, 1, 1;
19: 1, 0, 18, 0, 32670332, 0, 3727, 0,0, 0;
20: 1, 1, 24, 97723, 456028489, 1125022326, 483012, 741, 13, 1, 1;
21: 1, 0, 27, 0, 6636066134, 0, 69823723, 0, 1, 0, 0;
22: 1, 1, 34, 1436873, 100135577994, 3813549359275, 14836130862, 2887493, ?, 14, 1;
CROSSREFS
Not necessarily connected k-regular simple graphs with girth at least 4: A185314 (any k), this sequence (triangle); specified degree k: A008484 (k=2), A185334 (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).
Sequence in context: A362759 A123736 A358476 * A081389 A133685 A281492
KEYWORD
nonn,hard,tabf
AUTHOR
Jason Kimberley, Jan 19 2013
EXTENSIONS
E(10,2) corrected by the author, Mar 26 2013
a(32)=E(10,2) in b-file corrected as above by Andrew Howroyd, Feb 22 2018
STATUS
approved