A131088 2*A051731 - A054525 as infinite lower triangular matrices.

1, 3, 1, 3, 0, 1, 2, 3, 0, 1, 3, 0, 0, 0, 1, 1, 3, 3, 0, 0, 1, 3, 0, 0, 0, 0, 0, 1, 2, 2, 0, 3, 0, 0, 0, 1, 2, 0, 3, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 3, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 3, 0, 3, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson, Jun 14 2007

Keywords

• nonn
• tabl

Comments

Row sums = A131089.

A131090: (1, 3, 3, 2, 3, 1, 3, 2, 2, 1, ...) in every column interspersed with (k-1) zeros.

Examples

			First few rows of the triangle:
  1;
  3, 1;
  3, 0, 1;
  2, 3, 0, 1;
  3, 0, 0, 0, 1;
  1, 3, 3, 0, 0, 1
  3, 0, 0, 0, 0, 0, 1;
  2, 2, 0, 3, 0, 0, 0, 1;
  ...
		

Crossrefs

Cf. A129979 (left border), A131089 (row sums), A051731, A054525.

Programs

PARI

T(n,k) = 2*!(n%k) - if (!(n % k), moebius(n/k), 0);
row(n) = vector(n, k, T(n,k));
lista(nn) = for (n=1, nn, v = row(n); for (k=1, #v, print1(v[k], ", "))); \\ Michel Marcus, Feb 26 2022

Extensions

More terms from Michel Marcus, Feb 26 2022