A185304 Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 4.

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.

Links

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

Jason Kimberley, Not necessarily connected k-regular graphs with girth at least 4

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

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

Adjacent sequences: A185301 A185302 A185303 * A185305 A185306 A185307

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