A112899 A skew Pell-Pascal triangle.

1, 0, 2, 0, 1, 5, 0, 0, 4, 12, 0, 0, 1, 14, 29, 0, 0, 0, 6, 44, 70, 0, 0, 0, 1, 27, 131, 169, 0, 0, 0, 0, 8, 104, 376, 408, 0, 0, 0, 0, 1, 44, 366, 1052, 985, 0, 0, 0, 0, 0, 10, 200, 1212, 2888, 2378, 0, 0, 0, 0, 0, 1, 65, 810, 3842, 7813, 5741, 0, 0, 0, 0, 0, 0, 12, 340, 3032, 11784

Offset: 0

Author

Paul Barry, Oct 05 2005

Keywords

• easy
• nonn
• tabl

Comments

Main diagonal is A000129. Row sums are A002605. Column sums are A006190(n+1).

A skewed version of the Riordan array (1/(1-2x-x^2), x/(1-2x-x^2)), see A054456. - Philippe Deléham, Nov 21 2007

Triangle, read by rows, given by [0,1/2,-1/2,0,0,0,0,0,...] DELTA [2,1/2,-1/2,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 30 2010

Examples

			Rows begin:
  1;
  0,   2;
  0,   1,   5;
  0,   0,   4,  12;
  0,   0,   1,  14,  29;
  0,   0,   0,   6,  44,  70;
  0,   0,   0,   1,  27, 131, 169;
  0,   0,   0,   0,   8, 104, 376, 408;
		

Crossrefs

Cf. A111006, A112906. - Philippe Deléham, Jan 30 2010

Formula

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

T(n, k) = Sum_{j=0..floor((2*k-n)/2)} C(k-j, n-k)*C(2*k-n-j, j)*2^(2*k-2*j-n). [corrected by Jason Yuen, Jan 21 2025]

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