login
A185130
Irregular triangle E(n,g) counting not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly g.
4
1, 1, 1, 4, 2, 15, 5, 1, 71, 21, 2, 428, 103, 8, 1, 3406, 752, 48, 1, 34270, 7385, 450, 5, 418621, 91939, 5752, 32, 5937051, 1345933, 90555, 385, 94782437, 22170664, 1612917, 7573, 1, 1670327647, 401399440, 31297424, 181224, 3, 32090011476, 7887389438
OFFSET
2,4
COMMENTS
The first column is for girth exactly 3. The column for girth exactly g begins when 2n reaches A000066(g).
FORMULA
The n-th row is the sequence of differences of the n-th row of A185330:
E(n,g) = A185330(n,g) - A185330(n,g+1), once we have appended 0 to each row of A185330.
Hence the sum of the n-th row is A185330(n,3) = A005638(n).
EXAMPLE
1;
1, 1;
4, 2;
15, 5, 1;
71, 21, 2;
428, 103, 8, 1;
3406, 752, 48, 1;
34270, 7385, 450, 5;
418621, 91939, 5752, 32;
5937051, 1345933, 90555, 385;
94782437, 22170664, 1612917, 7573, 1;
1670327647, 401399440, 31297424, 181224, 3;
32090011476, 7887389438, 652159986, 4624481, 21;
666351752261, 166897766824, 14499787794, 122089999, 545, 1;
14859579573845, 3781593764772, 342646826428, 3328899592, 30368, 0;
CROSSREFS
Initial columns of this triangle: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).
Sequence in context: A019061 A019012 A154333 * A261870 A325516 A299789
KEYWORD
nonn,hard,tabf
AUTHOR
Jason Kimberley, Dec 26 2012
STATUS
approved