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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,19

LINKS

Jason Kimberley, Table of i, a(i)=D(n,k) for i = 2..145 (n = 2..24)

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

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: A216228 A291957 A143063 * A275964 A284272 A175070

Adjacent sequences:  A210700 A210701 A210702 * A210704 A210705 A210706

KEYWORD

nonn,hard,tabf

AUTHOR

Jason Kimberley, Jan 21 2013

STATUS

approved

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Last modified May 19 10:36 EDT 2019. Contains 323390 sequences. (Running on oeis4.)