A154388 Triangle T(n,k), 0<=k<=n, read by rows given by [0,1,-1,0,0,0,0,0,0,0,...] DELTA [1,-1,-1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Formula

Sum_{k=0..n} T(n,k)*x^(n-k) = A135528(n+1), A000012(n), A040001(n), A153284(n+1) for x = 0,1,2,3 respectively.

G.f.: (1+y*x+(y-y^2)*x^2)/(1-y^2*x^2). - Philippe Deléham, Dec 17 2011

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A000012(n), A158302(n) for x = 0, 1, 2 respectively. - Philippe Deléham, Dec 17 2011

Example

Triangle begins:
  1;
  0, 1;
  0, 1, 0;
  0, 0, 0, 1;
  0, 0, 0, 1, 0;
  0, 0, 0, 0, 0, 1; ...

Crossrefs

Sequence in context: A089806 A274719 A014069 * A285136 A029694 A171894

Adjacent sequences: A154385 A154386 A154387 * A154389 A154390 A154391

Keyword

nonn,tabl

Author

Philippe Deléham, Jan 08 2009

Status

approved