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

0,3

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

Links

Table of n, a(n) for n=0..75.

Formula

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

T(n, k) = Sum_{j=0..floor((2k-n)/2)} C(k-j, n-k)*C(2k-n, j)*2^(2k-2j-n)};

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

Example

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

Sequence in context: A016584 A293961 A364228 * A212808 A337085 A209687

Adjacent sequences: A112896 A112897 A112898 * A112900 A112901 A112902

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 05 2005

Status

approved