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A333893 Array read by antidiagonals: T(n,k) is the number of unlabeled loopless multigraphs with n nodes of degree k or less. 9
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 4, 5, 3, 1, 1, 1, 5, 8, 10, 3, 1, 1, 1, 6, 14, 26, 16, 4, 1, 1, 1, 7, 20, 61, 60, 29, 4, 1, 1, 1, 8, 30, 128, 243, 184, 45, 5, 1, 1, 1, 9, 40, 254, 800, 1228, 488, 75, 5, 1, 1, 1, 10, 55, 467, 2518, 7252, 6684, 1509, 115, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

T(n,k) is the number of non-isomorphic n X n nonnegative integer symmetric matrices with all row and column sums equal to k and isomorphism being up to simultaneous permutation of rows and columns. The case that allows independent permutations of rows and columns is covered by A333737.

Terms may be computed without generating each graph by enumerating the number of graphs by degree sequence using dynamic programming. A PARI program showing this technique for the labeled case is given in A188403. Burnside's lemma as applied in A192517 can be used to extend this method to the unlabeled case.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..377 (antidiagonals 0..26)

EXAMPLE

Array begins:

==============================================

n\k | 0 1  2   3    4     5      6       7

----+-----------------------------------------

  0 | 1 1  1   1    1     1      1       1 ...

  1 | 1 1  1   1    1     1      1       1 ...

  2 | 1 2  3   4    5     6      7       8 ...

  3 | 1 2  5   8   14    20     30      40 ...

  4 | 1 3 10  26   61   128    254     467 ...

  5 | 1 3 16  60  243   800   2518    6999 ...

  6 | 1 4 29 184 1228  7252  38194  175369 ...

  7 | 1 4 45 488 6684 78063 772243 6254652 ...

  ...

CROSSREFS

Rows n=0..4 are A000012, A000012, A000027(n+1), A006918(n+1), A333897.

Columns k=0..5 are A000012, A008619, A000990, A333894, A333895, A333896.

Cf. A188403, A192517, A263293, A333161, A333330, A333737, A334546.

Sequence in context: A123320 A054123 A119269 * A225630 A129713 A096669

Adjacent sequences:  A333890 A333891 A333892 * A333894 A333895 A333896

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Apr 08 2020

STATUS

approved

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Last modified January 17 23:51 EST 2022. Contains 350410 sequences. (Running on oeis4.)