A177978 Triangle T(n,k) read by rows: A051731(n,k) - A051731(n-1,k).

1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -1, 0, -1, 1, 0, 1, 1, 0, -1, 1, 0, -1, -1, 0, 0, -1, 1, 0, 1, 0, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, 0, 0, -1, 1, 0, 1, -1, 0, 1, 0, 0, 0, -1, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, -1, 1, 0, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 1

Offset: 1

Author

Mats Granvik, May 16 2010

Keywords

• sign
• tabl

Comments

The recurrence for this triangle is similar to the recurrence in A177517. Cumulative column sums give table A051731.

Examples

			Triangle begins:
  1;
  0,  1;
  0, -1,  1;
  0,  1, -1,  1;
  0, -1,  0, -1,  1;
  0,  1,  1,  0, -1,  1;
  0, -1, -1,  0,  0, -1,  1;
  0,  1,  0,  1,  0,  0, -1,  1;
  0, -1,  1, -1,  0,  0,  0, -1,  1;
  0,  1, -1,  0,  1,  0,  0,  0, -1,  1;
  0, -1,  0,  0, -1,  0,  0,  0,  0, -1,  1;
  0,  1,  1,  1,  0,  1,  0,  0,  0,  0, -1,  1;
  0, -1, -1, -1,  0, -1,  0,  0,  0,  0,  0, -1,  1;
  0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0, -1,  1;
		

Crossrefs

Matrix inverse of A134540. Cf. A177517.

Formula

T(n,1)=A000007, k > 1: T(n,k) = (Sum_{i=1..k-1} T(n-i,k-1)) - (Sum_{i=1..k-1} T(n-i,k)).

Extensions

Typo in sequence (erroneous comma) corrected by N. J. A. Sloane, May 22 2010

Edited by Mats Granvik, Dec 11 2010