A112883 A skew Jacobsthal-Pascal matrix.

1, 0, 1, 0, 1, 3, 0, 0, 2, 5, 0, 0, 1, 7, 11, 0, 0, 0, 3, 16, 21, 0, 0, 0, 1, 12, 41, 43, 0, 0, 0, 0, 4, 34, 94, 85, 0, 0, 0, 0, 1, 18, 99, 219, 171, 0, 0, 0, 0, 0, 5, 60, 261, 492, 341, 0, 0, 0, 0, 0, 1, 25, 195, 678, 1101, 683, 0, 0, 0, 0, 0, 0, 6, 95, 576, 1692, 2426, 1365, 0, 0, 0, 0, 0

Offset: 0

Author

Paul Barry, Oct 05 2005

Keywords

• easy
• nonn
• tabl

Comments

T(n,n) is A001045(n), row sums are A006130, column sums are A002605. Compare with [0,1,-1,0,0,..] DELTA [1,2,-2,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-x-2x^2),x/(1-x-2x^2)) (A073370).

Modulo 2, this sequence gives A106344. - Philippe Deléham, Dec 18 2008

Examples

			Rows begin
  1;
  0, 1;
  0, 1, 3;
  0, 0, 2, 5;
  0, 0, 1, 7, 11;
  0, 0, 0, 3, 16, 21;
  0, 0, 0, 1, 12, 41, 43;
  0, 0, 0, 0,  4, 34, 94,  85;
  0, 0, 0, 0,  1, 18, 99, 219, 171;
  0, 0, 0, 0,  0,  5, 60, 261, 492,  341;
  0, 0, 0, 0,  0,  1, 25, 195, 678, 1101, 683;
		

Crossrefs

Cf. A111006.

Formula

From Philippe Deléham: (Start)

G.f.: 1/(1-yx(1-x)-2x^2*y*2);

Number triangle T(n, k) = Sum_{j=0..2k-n} C(n-k+j, n-k)*C(j, 2k-n-j)*2^(2k-n-j);

T(n, k) = A073370(k, n-k); T(n, k) = T(n-1, k-1) + T(n-2, k-1) + 2*T(n-2, k-2). (End)