A360491 Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [5n] into 5-element subsets {i, i+k, i+2k, i+3k, i+4k} 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, 10, 19, 24, 21, 1, 1, 2, 4, 10, 20, 41, 44, 34, 1, 1, 2, 4, 10, 21, 43, 84, 81, 55, 1, 1, 2, 4, 10, 21, 58, 89, 180, 149, 89, 1, 1, 2, 4, 10, 21, 59, 120, 192, 372, 274, 144, 1

Offset: 1

Author

Peter Dolland, Feb 09 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,   10,   10,   10,   10,   10, ...
  1,   8,  13,   19,   20,   21,   21,   21,   21, ...
  1,  13,  24,   41,   43,   58,   59,   59,   59, ...
  1,  21,  44,   84,   89,  120,  124,  125,  125, ...
  1,  34,  81,  180,  192,  280,  289,  344,  349, ...
  1,  55, 149,  372,  404,  626,  648,  759,  811, ...
  1,  89, 274,  785,  860, 1454, 1510, 1877, 1996, ...
  1, 144, 504, 1637, 1816, 3272, 3414, 4263, 4565, ...
  ...
		

Crossrefs

Main diagonal is A349430.

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

Cf. A104431, A104443, A360333..A360335, A360492, A360493.

Formula

A(n,m) = A104431(n) = A104443(n,5) for m >= floor((5n - 1) / 4).