A130888 Triangle read by rows, A051731(n,k) dot (1, 3, 7, 15, ...) with like numbers of terms.

1, 1, 3, 1, 0, 7, 1, 3, 0, 15, 1, 0, 0, 0, 31, 1, 3, 7, 0, 0, 63, 1, 0, 0, 0, 0, 0, 127, 1, 3, 0, 15, 0, 0, 0, 255

Offset: 1

Author

Gary W. Adamson, Jun 07 2007

Keywords

• nonn
• tabl

Comments

Row sums = A130887: (1, 4, 8, 19, 32, 74, 128, 274, 519, 1058, ...).

Examples

			First few rows of the triangle:
  1;
  1,  3;
  1,  0,  7;
  1,  3,  0, 15;
  1,  0,  0,  0, 31;
  1,  3,  7,  0,  0, 63;
  ...
Row 4 = (1, 3, 0, 15) = (1, 1, 0, 1) dot (1, 3, 7, 15); where (1, 1, 0, 1) = row 4 of A051731.
		

Crossrefs

Cf. A051731, A130887.

Formula

Triangle read by rows, dot product of each row of A051731 and the same number of terms in the series (1, 3, 7, 15, ...).

G.f.: Sum_{k>0} (2^k-1)*(x*y)^k/(1-x^k). - Vladeta Jovovic, Dec 02 2008