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A210703
Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth exactly 3.
7
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 3, 0, 1, 0, 0, 4, 8, 3, 1, 0, 0, 5, 0, 8, 0, 0, 0, 6, 29, 25, 3, 1, 0, 0, 9, 0, 88, 0, 1, 0, 0, 10, 138, 377, 66, 5, 1, 0, 0, 13, 0, 2026, 0, 25, 0, 0, 0, 17, 774, 13349, 8029, 297, 5, 1, 0, 0, 21, 0, 104593, 0, 8199, 0, 1, 0, 0, 25, 5678, 930571, 3484759, 377004, 1562, 7, 1
OFFSET
2,19
FORMULA
D(n,k) = A068933(n,k) - A185204(n,k) [the former is padded to be a tabl but the latter is a tabf].
D(n,k) = A185643(n,k) - A186733(n,k) [both are tabl but the result is tabf].
EXAMPLE
2: 0;
3: 0;
4: 0, 0;
5: 0, 0;
6: 0, 0, 1;
7: 0, 0, 1;
8: 0, 0, 1, 1;
9: 0, 0, 2, 0;
10: 0, 0, 2, 2, 1;
11: 0, 0, 3, 0, 1;
12: 0, 0, 4, 8, 3, 1;
13: 0, 0, 5, 0, 8, 0;
14: 0, 0, 6, 29, 25, 3, 1;
15: 0, 0, 9, 0, 88, 0, 1;
16: 0, 0, 10, 138, 377, 66, 5, 1;
17: 0, 0, 13, 0, 2026, 0, 25, 0;
18: 0, 0, 17, 774, 13349, 8029, 297, 5, 1;
19: 0, 0, 21, 0, 104593, 0, 8199, 0, 1;
20: 0, 0, 25, 5678, 930571, 3484759, 377004, 1562, 7, 1;
21: 0, 0, 33, 0, 9124627, 0, 22014143, 0, 100, 0;
22: 0, 0, 39, 53324, 96699740, 2595985769, 1493574756, 21617036, 10901, 9, 1;
23: 0, 0, 49, 0, 1095467916, 0, 114880777582, 0, 3470736, 0, 1;
24: 0, 0, 60, 622716, 13175254799, 2815099031409, 9919463450854, 733460349818, 1473822243, 88238, 11, 1;
CROSSREFS
The sum of the n-th row is A210713(n).
Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), this sequence (triangle); for a fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).
Sequence in context: A374202 A291957 A143063 * A340455 A275964 A284272
KEYWORD
nonn,hard,tabf
AUTHOR
Jason Kimberley, Jan 21 2013
STATUS
approved