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

1,4

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

Links

Table of n, a(n) for n=1..55.

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

Example

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.

Sequence in context: A282290 A178795 A123185 * A141071 A004648 A265848

Adjacent sequences: A133566 A133567 A133568 * A133570 A133571 A133572

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 16 2007

Status

approved