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A333330 Array read by antidiagonals: T(n,k) is the number of k-regular loopless multigraphs on n unlabeled nodes, n >= 0, k >= 0. 13
1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 3, 2, 1, 1, 1, 0, 1, 0, 4, 0, 4, 0, 1, 1, 0, 1, 1, 5, 7, 9, 4, 1, 1, 1, 0, 1, 0, 7, 0, 24, 0, 7, 0, 1, 1, 0, 1, 1, 8, 16, 54, 60, 32, 8, 1, 1, 1, 0, 1, 0, 10, 0, 128, 0, 240, 0, 12, 0, 1, 1, 0, 1, 1, 12, 37, 271, 955, 1753, 930, 135, 14, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,26
COMMENTS
Terms may be computed without generating each graph by enumerating the number of graphs by degree sequence. A PARI program showing this technique for graphs with labeled vertices is given in A333351. Burnside's lemma can be used to extend this method to the unlabeled case.
LINKS
EXAMPLE
Array begins:
=================================================
n\k | 0 1 2 3 4 5 6 7 8
----+--------------------------------------------
0 | 1 1 1 1 1 1 1 1 1 ...
1 | 1 0 0 0 0 0 0 0 0 ...
2 | 1 1 1 1 1 1 1 1 1 ...
3 | 1 0 1 0 1 0 1 0 1 ...
4 | 1 1 2 3 4 5 7 8 10 ...
5 | 1 0 2 0 7 0 16 0 37 ...
6 | 1 1 4 9 24 54 128 271 582 ...
7 | 1 0 4 0 60 0 955 0 12511 ...
8 | 1 1 7 32 240 1753 13467 90913 543779 ...
9 | 1 0 8 0 930 0 253373 0 35255015 ...
...
CROSSREFS
Columns k=0..8 are (with interspersed 0's for odd k): A000012, A000012, A002865, A129416, A129418, A129420, A129422, A129424, A129426.
Row n=4 is A001399.
Cf. A051031 (simple graphs), A167625 (with loops), A192517 (not necessarily regular), A328682 (connected), A333351 (labeled nodes).
Sequence in context: A326815 A117210 A060277 * A290825 A204688 A332038
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 15 2020
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)