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

0,8

Links

Table of n, a(n) for n=0..65.

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).

Example

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.

Sequence in context: A059594 A183760 A125678 * A106585 A057227 A335190

Adjacent sequences: A091559 A091560 A091561 * A091563 A091564 A091565

Keyword

nonn,easy,tabl

Author

Christian G. Bower, Jan 20 2004

Status

approved