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

0,6

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

Links

Table of n, a(n) for n=0..82.

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)

Example

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.

Sequence in context: A357317 A357236 A156548 * A117138 A292255 A362313

Adjacent sequences: A112880 A112881 A112882 * A112884 A112885 A112886

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 05 2005

Status

approved