A382956 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n * y^k] Product_{p prime} 1/(1 - x^p - y^p).

1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0, 1, 2, 0, 1, 1, 0, 2, 2, 0, 3, 2, 3, 0, 2, 3, 0, 3, 1, 1, 3, 0, 3, 3, 0, 5, 3, 6, 3, 5, 0, 3, 4, 0, 6, 4, 4, 4, 4, 6, 0, 4, 5, 0, 8, 4, 11, 8, 11, 4, 8, 0, 5, 6, 0, 10, 6, 10, 9, 9, 10, 6, 10, 0, 6, 7, 0, 13, 8, 19, 13, 28, 13, 19, 8, 13, 0, 7

Offset

0,13

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Formula

A(n,k) = A(k,n).

Example

Square array begins:
  1, 0,  1, 1,  1,  2,  2,  3,   3,   4, ...
  0, 0,  0, 0,  0,  0,  0,  0,   0,   0, ...
  1, 0,  2, 1,  3,  3,  5,  6,   8,  10, ...
  1, 0,  1, 2,  1,  3,  4,  4,   6,   8, ...
  1, 0,  3, 1,  6,  4, 11, 10,  19,  20, ...
  2, 0,  3, 3,  4,  8,  9, 13,  17,  22, ...
  2, 0,  5, 4, 11,  9, 28, 20,  50,  50, ...
  3, 0,  6, 4, 10, 13, 20, 28,  38,  51, ...
  3, 0,  8, 6, 19, 17, 50, 38, 104,  92, ...
  4, 0, 10, 8, 20, 22, 50, 51,  92, 122, ...

Crossrefs

Columns k=0..1 give A000607, A000004.

Cf. A322210, A382955.

Sequence in context: A294168 A299196 A227698 * A331466 A166124 A134979

Adjacent sequences: A382953 A382954 A382955 * A382957 A382958 A382959

Keyword

nonn,tabl

Author

Seiichi Manyama, Apr 10 2025

Status

approved