A091562 Triangle read by rows, related to Pascal's triangle, starting with 1, 0, 0.

1, 0, 0, 1, 1, 1, 1, 2, 2, 1, 2, 5, 7, 5, 2, 3, 10, 17, 17, 10, 3, 5, 20, 41, 51, 41, 20, 5, 8, 38, 91, 136, 136, 91, 38, 8, 13, 71, 195, 339, 405, 339, 195, 71, 13, 21, 130, 403, 799, 1107, 1107, 799, 403, 130, 21, 34, 235, 812, 1807, 2845, 3297, 2845, 1807, 812, 235, 34

Offset: 0

Author

Christian G. Bower, Jan 20 2004

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins:
  1;
  0,0;
  1,1,1;
  1,2,2,1;
  2,5,7,5,2;
  ...
		

Crossrefs

Row sums: A054878, column 0: A000045(n-1), column 1: A001629.

Cf. A090171, A090172, A090173, A090174, A091533, A205575 (same recurrence).

Cf. A090172.

Formula

T(n, k) = T(n-1, k) + T(n-1, k-1) + T(n-2, k) + T(n-2, k-1) + T(n-2, k-2) for n >= 2, k >= 0, with initial conditions specified by first two rows.

G.f.: A(x, y) = (1-x-x*y)/(1-x-x*y-x^2-x^2*y-x^2*y^2).