A360334 Array read by antidiagonals downwards: A(n,m) = number of set partitions of [3n] into 3-element subsets {i, i+k, i+2k} with 1 <= k <= m.

1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 2, 5, 7, 8, 1, 1, 2, 5, 12, 13, 13, 1, 1, 2, 5, 15, 25, 24, 21, 1, 1, 2, 5, 15, 35, 56, 44, 34, 1, 1, 2, 5, 15, 46, 84, 126, 81, 55, 1, 1, 2, 5, 15, 55, 129, 211, 281, 149, 89, 1, 1, 2, 5, 15, 55, 185, 346, 537, 625, 274, 144, 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,   5,    5,    5,    5,     5,     5, ...
  1,  5,   7,  12,   15,   15,   15,    15,    15, ...
  1,  8,  13,  25,   35,   46,   55,    55,    55, ...
  1, 13,  24,  56,   84,  129,  185,   232,   232, ...
  1, 21,  44, 126,  211,  346,  567,   831,  1040, ...
  1, 34,  81, 281,  537,  973, 1781,  2920,  4242, ...
  1, 55, 149, 625, 1352, 2732, 5643, 10213, 16110, ...
  ...
		

Crossrefs

Main diagonal is A334250.

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

Cf. A104429, A104443, A360333, A360335.

Formula

A(n,m) = A104429(n) = A104443(n,3) for m >= floor((3n - 1) / 2).