A360333 Array read by antidiagonals downwards: A(n,m) = number of set partitions of [4n] into 4-element subsets {i, i+k, i+2k, i+3k} with 1 <= k <= m.

1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 2, 4, 7, 8, 1, 1, 2, 4, 10, 13, 13, 1, 1, 2, 4, 11, 19, 24, 21, 1, 1, 2, 4, 11, 22, 41, 44, 34, 1, 1, 2, 4, 11, 23, 48, 84, 81, 55, 1, 1, 2, 4, 11, 23, 64, 101, 180, 149, 89, 1

Offset: 1

Author

Peter Dolland, Feb 03 2023

Keywords

• nonn
• tabl

Examples

			Square array begins:
  1,  1,   1,   1,   1,   1,   1,   1,    1, ...
  1,  2,   2,   2,   2,   2,   2,   2,    2, ...
  1,  3,   4,   4,   4,   4,   4,   4,    4, ...
  1,  5,   7,  10,  11,  11,  11,  11,   11, ...
  1,  8,  13,  19,  22,  23,  23,  23,   23, ...
  1, 13,  24,  41,  48,  64,  68,  68,   68, ...
  1, 21,  44,  84, 101, 134, 147, 148,  161, ...
  1, 34,  81, 180, 225, 318, 353, 409,  444, ...
  1, 55, 149, 372, 485, 721, 814, 929, 1092, ...
  ...
		

Crossrefs

Main diagonal is A337520.

Columns 1..3 are A000012, A000045(n+1), A000073(n+2).

Cf. A104430, A104443, A360334, A360335.

Formula

A(n,m) = A104430(n) = A104443(n,4) for m >= floor((4n - 1) / 3).