A180262 Triangle by rows, generated from a triangle with (1,2,1,1,1,...) in every column.

1, 2, 1, 1, 2, 3, 1, 1, 6, 6, 1, 1, 3, 12, 14, 1, 1, 3, 6, 28, 31, 1, 1, 3, 6, 14, 62, 70, 1, 1, 3, 6, 14, 31, 140, 157, 1, 1, 3, 6, 14, 31, 70, 314, 353, 1, 1, 3, 6, 14, 31, 70, 157, 706, 793, 1, 1, 3, 6, 14, 31, 70, 157, 353, 1586, 1782

Offset: 0

Author

Gary W. Adamson, Aug 21 2010

Keywords

• nonn
• tabl

Comments

Row sums = A006356: (1, 3, 6, 14, 31, 70, 157, 353,...).

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

Examples

			First few rows of the triangle:
  1;
  2, 1;
  1, 2, 3;
  1, 1, 6,  6;
  1, 1, 3, 12, 14;
  1, 1, 3,  6, 28, 31;
  1, 1, 3,  6, 14, 62,  70;
  1, 1, 3,  6, 14, 31, 140, 157;
  1, 1, 3,  6, 14, 31,  70, 314, 353;
  1, 1, 3,  6, 14, 31,  70, 157, 706,  793;
  1, 1, 3,  6, 14, 31,  70, 157, 353, 1586, 1782;
  1, 1, 3,  6, 14, 31,  70, 157, 353,  793, 3564, 4004;
  1, 1, 3,  6, 14, 31,  70, 157, 353,  793, 1782, 8008,  8997;
  1, 1, 3,  6, 14, 31,  70, 157, 353,  793, 1782, 4004, 17994, 20216;
  ...
Example: row 3 of the triangle = (1, 1, 6, 6) = termwise products of (1, 1, 2, 1) and (1, 1, 3, 6).
		

Crossrefs

Cf. A006356.

Formula

Let M be an infinite Toeplitz lower triangular matrix with (1,2,1,1,1,..) in every column. A180262 = M * a diagonalized variant of A006356 such that the main diagonal = A006356 prefaced with a 1: (1, 1, 3, 6, 14, 31,...) and the rest zeros.