A353434 Array read by descending antidiagonals: T(n,m) is the number of sequences of length n >= 0 with elements in 1..m-1 such that no iterated difference is divisible by m >= 1.

1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 6, 2, 0, 0, 1, 5, 12, 8, 2, 0, 0, 1, 6, 20, 28, 6, 2, 0, 0, 1, 7, 30, 64, 48, 6, 2, 0, 0, 1, 8, 42, 126, 164, 60, 6, 2, 0, 0, 1, 9, 56, 216, 444, 336, 60, 6, 2, 0, 0, 1, 10, 72, 344, 954, 1350, 552, 52, 6, 2, 0, 0

Offset: 0

Author

Pontus von Brömssen, Apr 21 2022

Keywords

• nonn
• tabl

Examples

			Array begins:
  n\m| 1  2  3  4  5    6     7      8       9       10
  ---+-------------------------------------------------
   0 | 1  1  1  1  1    1     1      1       1        1
   1 | 0  1  2  3  4    5     6      7       8        9
   2 | 0  0  2  6 12   20    30     42      56       72
   3 | 0  0  2  8 28   64   126    216     344      512
   4 | 0  0  2  6 48  164   444    954    1850     3240
   5 | 0  0  2  6 60  336  1350   3630    8732    18240
   6 | 0  0  2  6 60  552  3582  11898   36290    90624
   7 | 0  0  2  6 52  772  8550  33862  133628   398048
   8 | 0  0  2  6 48 1054 17364  83946  437666  1545468
   9 | 0  0  2  6 48 1614 30126 182134 1278314  5300824
  10 | 0  0  2  6 48 2740 44922 346638 3321680 16079024
		

Links

• Pontus von Brömssen, Plot of T(n,7) for 0 <= n <= 200

Crossrefs

Cf. A350529, A353433, A353436.

Rows: A000012 (n=0), A001477 (n=1), A002378 (n=2), A245996 (n=3).

Columns: A000007 (m=1), A019590 (m=2), A040000 (m=3).

Formula

T(n,m) = A353433(n,m) if m is prime.

T(n,1) = 0 for n >= 1.

T(n,2) = 0 for n >= 2.

T(n,3) = 2 for n >= 1.

T(n,4) = 6 for n >= 4.

T(n,5) = 48 for n >= 8.

It appears that T(n,7) = T(n+42,7) for n >= 56. (See linked plot.)