A349430 -id:A349430 - cp's OEIS frontend

A104431 Number of ways to split 1, 2, 3, ..., 5n into n arithmetic progressions each with 5 terms.

1, 1, 2, 4, 10, 21, 59, 125, 349, 848, 2224, 5210, 15720, 37096, 98241, 245251, 684475, 1703174, 4915084, 12024901, 33594399

Offset: 0

Jonas Wallgren, Mar 17 2005

Cf. A104429-A104430, A104432-A104443, A349430.

a(11)-a(18) from Alois P. Heinz, Dec 28 2011

a(19)-a(20) from Alois P. Heinz, Nov 18 2021

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.

Original entry on oeis.org

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

Peter Dolland, Feb 09 2023

			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, ...
  ...

Main diagonal is A349430.
Columns 1..3 are A000012, A000045(n+1), A000073(n+2).
Cf. A104431, A104443, A360333..A360335, A360492, A360493.

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

cp's OEIS Frontend

A104431 Number of ways to split 1, 2, 3, ..., 5n into n arithmetic progressions each with 5 terms.

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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.

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