A133569 A133566 * A007318 as infinite lower triangular matrices.

1, 1, 1, 2, 3, 1, 1, 3, 3, 1, 2, 7, 9, 5, 1, 1, 5, 10, 10, 5, 1, 2, 11, 25, 30, 20, 7, 1, 1, 7, 21, 35, 35, 21, 7, 1, 2, 15, 49, 91, 105, 77, 35, 9, 1, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1

Offset: 1

Author

Gary W. Adamson, Sep 16 2007

Keywords

• nonn
• tabl

Comments

Row sums = A122756: (1, 2, 6, 8, 24, 32, 96, ...).

With offset (0,4); triangle T(n,k), 0 <= k <= n, given by [1,1,-3,1,0,0,0,0,0,0,0,...] DELTA [1,0,-2,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 15 2007

Examples

			First few rows of the triangle:
  1;
  1,  1;
  2,  3,  1;
  1,  3,  3,  1;
  2,  7,  9,  5,  1;
  1,  5, 10, 10,  5,  1;
  2, 11, 25, 30, 20,  7,  1;
  1,  7, 21, 35, 35, 21,  7,  1;
  ...
		

Crossrefs

Cf. A133566, A122756.

Formula

T(n,k) = T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2), T(0,0) = 1, T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(2,2) = 1, T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, Sep 17 2014

G.f.: (-1-x-x*y-x^2-x^2*y)/((x*y+1+x)*(-1+x+x*y)). - R. J. Mathar, Aug 12 2015