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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
OFFSET
1,25
COMMENTS
Row sums give A185315.
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
KEYWORD
nonn,hard,tabf
AUTHOR
Jason Kimberley, Feb 21 2013
STATUS
approved