A167948 Triangle read by rows, A101688 * (an infinite lower triangular matrix with A002083 as the main diagonal and the rest zeros).

1, 0, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 2, 3, 0, 0, 0, 2, 3, 6, 0, 0, 0, 2, 3, 6, 11, 0, 0, 0, 0, 3, 6, 11, 22, 0, 0, 0, 0, 3, 6, 11, 22, 42, 0, 0, 0, 0, 0, 6, 11, 22, 42, 84, 0, 0, 0, 0, 0, 6, 11, 22, 42, 84, 165, 0, 0, 0, 0, 0, 0, 11, 22, 42, 84, 165, 330

Offset: 1

Author

Gary W. Adamson, Nov 15 2009

Keywords

• nonn
• tabl

Comments

Row sums = A002083(n+1): (1, 1, 2, 3, 6, 11, 22, 42, 84, 165,...).

Sum of n-th row terms = rightmost term of next row.

Eigensequence of triangle A101688 = A002083 starting with offset 1: (1, 1, 2, 3, 6, 11, 22, 42,...).

Examples

			First few rows of the triangle:
  1;
  0, 1;
  0, 1, 1;
  0, 0, 1, 2;
  0, 0, 1, 2, 3;
  0, 0, 0, 2, 3, 6;
  0, 0, 0, 2, 3, 6, 11;
  0, 0, 0, 0, 3, 6, 11, 22;
  0, 0, 0, 0, 3, 6, 11, 22, 42;
  0, 0, 0, 0, 0, 6, 11, 22, 42, 84;
  0, 0, 0, 0, 0, 6, 11, 22, 42, 84, 165;
  0, 0, 0, 0, 0, 0, 11, 22, 42, 84, 165, 330;
  0, 0, 0, 0, 0, 0, 11, 22, 42, 84, 165, 330, 654;
  0, 0, 0, 0, 0, 0, .0, 22, 42, 84, 165, 330, 654, 1308;
  0, 0, 0, 0, 0, 0, .0, 22, 42, 84, 165, 330, 654, 1308, 2605;
  ...
		

Crossrefs

Cf. A101688, A002083.

Formula

Equals M * Q, where M = triangle A101688, Q = an infinite lower triangular matrix with (1, 1, 1, 2, 3, 6, 11, 22, 42,...) as the main diagonal and the rest zeros.