A185305 Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 5.

1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 2, 0, 1, 1, 3, 2, 1, 0, 3, 0, 1, 1, 4, 9, 1, 0, 5, 0, 1, 1, 6, 49, 1, 0, 7, 0, 1, 1, 9, 455, 1, 0, 10, 0, 1, 1, 1, 13, 5784, 2, 1, 0, 15, 0, 8, 1, 1, 18, 90940, 131, 1, 0, 21, 0, 3917, 1, 1, 26, 1620491, 123859

Offset

1,25

Comments

Row sums give A185315.

Links

Jason Kimberley, Table of n, a(i)=E(n,k) for i = 1..108 (n = 1..28)

Jason Kimberley, Not necessarily connected k-regular graphs with girth at least 5

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

Formula

E(n,k) = A186715(n,k) + A185205(n,k).

Example

01: 1;
02: 1, 1;
03: 1, 0;
04: 1, 1;
05: 1, 0, 1;
06: 1, 1, 1;
07: 1, 0, 1;
08: 1, 1, 1;
09: 1, 0, 1;
10: 1, 1, 2, 1;
11: 1, 0, 2, 0;
12: 1, 1, 3, 2;
13: 1, 0, 3, 0;
14: 1, 1, 4, 9;
15: 1, 0, 5, 0;
16: 1, 1, 6, 49;
17: 1, 0, 7, 0;
18: 1, 1, 9, 455;
19: 1, 0, 10, 0, 1;
20: 1, 1, 13, 5784, 2;
21: 1, 0, 15, 0, 8;
22: 1, 1, 18, 90940, 131;
23: 1, 0, 21, 0, 3917;
24: 1, 1, 26, 1620491, 123859;
25: 1, 0, 30, 0, 4131991;
26: 1, 1, 36, 31478649, 132160608;
27: 1, 0, 42, 0, 4018022149;
28: 1, 1, 50, 656784488, 118369811960;

Crossrefs

Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), this sequence (triangle); specified degree k: A185325 (k=2), A185335 (k=3).

Sequence in context: A253559 A136167 A140748 * A259875 A070821 A165890

Adjacent sequences: A185302 A185303 A185304 * A185306 A185307 A185308

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Feb 21 2013

Status

approved