A360493 Square of A(n,m) read by antidiagonals. A(n,m) = number of set partitions of [7n] into 7-element subsets {i, i+k, i+2k, i+3k, i+4k, i+5k, i+6k} 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, 20, 43, 84, 81, 55, 1, 1, 2, 4, 10, 20, 56, 89, 180, 149, 89, 1, 1, 2, 4, 10, 20, 56, 115, 192, 372, 274, 144, 1

Offset

1,5

Links

Table of n, a(n) for n=1..78.

Formula

A(n,m) = A104433(n) = A104443(n,7) for m >= floor((7*n - 1) / 6).

Example

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,   20,   20,   20,    20, ...
  1,  13,  24,   41,   43,   56,   56,   56,    56, ...
  1,  21,  44,   84,   89,  115,  116,  117,   117, ...
  1,  34,  81,  180,  192,  267,  269,  322,   323, ...
  1,  55, 149,  372,  404,  592,  597,  704,   744, ...
  1,  89, 274,  785,  860, 1372, 1384, 1741,  1822, ...
  1, 144, 504, 1637, 1816, 3028, 3060, 3886,  4088, ...
  1, 233, 927, 3442, 3857, 7038, 7114, 9742, 10374, ...
  ...

Crossrefs

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

Cf. A104433, A104443, A360333..A360335, A360491, A360492.

Sequence in context: A180562 A199711 A048887 * A360492 A360491 A360333

Adjacent sequences: A360490 A360491 A360492 * A360494 A360495 A360496

Keyword

nonn,tabl

Author

Peter Dolland, Feb 09 2023

Status

approved