|
| |
|
|
A185305
|
|
Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 5.
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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: A105469 A136167 A140748 * A070821 A165890 A051632
Adjacent sequences: A185302 A185303 A185304 * A185307 A185308 A185309
|
|
|
KEYWORD
|
nonn,hard,tabf
|
|
|
AUTHOR
|
Jason Kimberley, Feb 21 2013
|
|
|
STATUS
|
approved
|
| |
|
|
