A181650 Inverse of number triangle A070909.

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

Offset: 0

Author

Paul Barry, Nov 03 2010

Keywords

• easy
• sign
• tabl

Comments

Generalized (conditional) Riordan array with k-th column generated by x^k*(1-x-x^2) if k is even, x^k otherwise.

Triangle T(n,k), read by rows, given by (-1,2,-1/2,-1/2,0,0,0,0,0,0,0,...) DELTA (1,0,-1,0,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 19 2011

Double Riordan array (1 - x - x^2; x/(1 - x - x^2), x*(1 - x - x^2)) as defined in Davenport et al. - Peter Bala, Aug 15 2021

Examples

			Triangle begins
   1,
  -1,  1,
  -1,  0,  1,
   0,  0, -1,  1,
   0,  0, -1,  0,  1,
   0,  0,  0,  0, -1,  1,
   0,  0,  0,  0, -1,  0,  1,
   0,  0,  0,  0,  0,  0, -1,  1,
   0,  0,  0,  0,  0,  0, -1,  0,  1,
   0,  0,  0,  0,  0,  0,  0,  0, -1,  1,
   0,  0,  0,  0,  0,  0,  0,  0, -1,  0,  1
Production matrix begins
  -1,  1,
  -2,  1,  1,
  -1,  1, -1,  1,
  -1,  1, -2,  1,  1,
  -1,  1, -1,  1, -1,  1,
  -1,  1, -1,  1, -2,  1,  1,
  -1,  1, -1,  1, -1,  1, -1,  1,
  -1,  1, -1,  1, -1,  1, -2,  1,  1,
  -1,  1, -1,  1, -1,  1, -1,  1, -1,  1
		

Links

• D. E. Davenport, L. W. Shapiro and L. C. Woodson, The Double Riordan Group, The Electronic Journal of Combinatorics, 18(2) (2012).

Crossrefs

Cf. A084221, A084938.

Formula

G.f.: (1+(y-1)*x-x^2)/((1-y*x)*(1+y*x)). - Philippe Deléham, Nov 19 2011