A333397 - OEIS

A333397

Array read by antidiagonals: T(n,k) is the number of connected k-regular multigraphs on n unlabeled nodes, loops allowed, n >= 0, k >= 0.

1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 3, 4, 5, 1, 0, 0, 1, 0, 3, 0, 10, 0, 1, 0, 0, 1, 1, 4, 9, 26, 28, 17, 1, 0, 0, 1, 0, 4, 0, 47, 0, 97, 0, 1, 0, 0, 1, 1, 5, 17, 91, 291, 639, 359, 71, 1, 0, 0, 1, 0, 5, 0, 149, 0, 2789, 0, 1635, 0, 1, 0, 0

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

OFFSET

0,18

COMMENTS

This sequence can be derived from A167625 by inverse Euler transform.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..405 (first 28 antidiagonals)

FORMULA

Column k is the inverse Euler transform of column k of A167625.

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 1 0 1 0 1 0 1 ...

2 | 0 1 1 2 2 3 3 4 4 ...

3 | 0 0 1 0 4 0 9 0 17 ...

4 | 0 0 1 5 10 26 47 91 149 ...

5 | 0 0 1 0 28 0 291 0 1934 ...

6 | 0 0 1 17 97 639 2789 12398 44821 ...

7 | 0 0 1 0 359 0 35646 0 1631629 ...

8 | 0 0 1 71 1635 40264 622457 8530044 89057367 ...

9 | 0 0 1 0 8296 0 14019433 0 6849428873 ...

...

CROSSREFS

Columns k=3..8 (with interspersed 0's for odd k) are: A005967, A085549, A129430, A129432, A129434, A129436.

Cf. A167625 (not necessarily connected), A322115 (not necessarily regular), A328682 (loopless), A333330.

Sequence in context: A065360 A352512 A364032 * A101676 A056560 A345415

Adjacent sequences: A333394 A333395 A333396 * A333398 A333399 A333400

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Mar 18 2020

STATUS

approved