A334546 Array read by antidiagonals: T(n,k) is the number of unlabeled connected loopless multigraphs with n nodes of degree k or less.

1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 0, 1, 1, 3, 2, 0, 0, 1, 1, 4, 4, 2, 0, 0, 1, 1, 5, 9, 12, 2, 0, 0, 1, 1, 6, 14, 37, 22, 2, 0, 0, 1, 1, 7, 23, 93, 146, 68, 2, 0, 0, 1, 1, 8, 32, 203, 602, 772, 166, 2, 0, 0, 1, 1, 9, 46, 399, 2126, 5847, 4449, 534, 2, 0, 0

Offset

0,13

Comments

This sequence may be derived from A333893 by inverse Euler transform.

Links

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

Formula

Column k is the inverse Euler transform of column k of A333893.

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 | 0 1 2   3    4     5      6       7 ...
  3 | 0 0 2   4    9    14     23      32 ...
  4 | 0 0 2  12   37    93    203     399 ...
  5 | 0 0 2  22  146   602   2126    6308 ...
  6 | 0 0 2  68  772  5847  34126  164965 ...
  7 | 0 0 2 166 4449 66289 716141 6021463 ...
  ...

Crossrefs

Columns k=3..5 are A243391, A289157, A334547.

Main diagonal is A334546.

Cf. A289987, A328682 (regular), A333893 (not necessarily connected).

Sequence in context: A323179 A320508 A164925 * A035671 A190164 A253938

Adjacent sequences: A334543 A334544 A334545 * A334547 A334548 A334549

Keyword

nonn,tabl

Author

Andrew Howroyd, May 05 2020

Status

approved