A382955 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 + x^p + y^p).

1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 2, 0, 2, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 2, 0, 2, 0, 1, 1, 0, 2

Offset

0,16

Links

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

Formula

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

Example

Square array begins:
  1, 0, 1, 1, 0, 2, 0, 2, 1, 1, ...
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
  1, 0, 0, 1, 0, 1, 0, 1, 1, 0, ...
  1, 0, 1, 0, 0, 1, 0, 2, 0, 1, ...
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
  2, 0, 1, 1, 0, 2, 0, 2, 0, 1, ...
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
  2, 0, 1, 2, 0, 2, 0, 2, 1, 0, ...
  1, 0, 1, 0, 0, 0, 0, 1, 0, 1, ...
  1, 0, 0, 1, 0, 1, 0, 0, 1, 0, ...

Crossrefs

Columns k=0..1 give A000586, A000004.

Main diagonal gives 2*A382871(n) (for n > 0).

Cf. A284593, A382956.

Sequence in context: A216266 A177416 A087606 * A271368 A116799 A057556

Adjacent sequences: A382952 A382953 A382954 * A382956 A382957 A382958

Keyword

nonn,tabl

Author

Seiichi Manyama, Apr 10 2025

Status

approved