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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 Andrew Howroyd, Table of n, a(n) for n = 0..350 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 Adjacent sequences:  A333327 A333328 A333329 * A333331 A333332 A333333 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Mar 15 2020 STATUS approved

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Last modified May 5 23:20 EDT 2021. Contains 343579 sequences. (Running on oeis4.)