A167371 Triangle, read by rows, given by [0,1,-1,0,0,0,0,0,0,0,0,...] DELTA [1,0,-1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

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

Offset

0,1

Comments

Diagonal sums: A060576.

A167374*A154325 formatted as lower triangular matrix. - Philippe Deléham, Nov 19 2009

Links

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

Formula

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A046698(n+1), A111286(n+1), A027327(n) for x= 0, 1, 2, 3 respectively.

G.f.: (1+x^2*y)/(1-x*y). - Philippe Deléham, Nov 09 2013

T(n,k) = T(n-1,k-1) for n > 2, T(0,0) = T(1,1) = T(2,1) = T(2,2) = 1, T(1,0) = T(2,0) = 0, T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, Nov 09 2013

Example

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

Crossrefs

Cf. A097806, A103451.

Sequence in context: A296212 A189921 A341346 * A127241 A087748 A117446

Adjacent sequences: A167368 A167369 A167370 * A167372 A167373 A167374

Keyword

nonn,tabl

Author

Philippe Deléham, Nov 02 2009

Status

approved