A128937 Triangle formed by reading A039598 mod 2.

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

Offset: 0

Author

Philippe Deléham, Apr 27 2007, May 02 2007

Keywords

• nonn
• tabl
• easy

Comments

Also triangle formed by reading triangles A052179, A053121, A124575, A126075, A126093.

Also triangle formed by reading A065600 mod 2. - Philippe Deléham, Oct 15 2007

Examples

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

Crossrefs

Cf. A048896 (row sums).

Programs

Maple

A039598 := proc(n,k)
        binomial(2*n,n-k)-binomial(2*n,n-k-2) ;
end proc:
A128937 := proc(n,k)
        modp(A039598(n,k),2) ;
end proc: # R. J. Mathar, Apr 21 2021

Formula

Sum_{k=0..n} T(n,k) = A048896(n).

Sum_{k=0..n} T(n,k)*2^(n-k) = A101692(n). - Philippe Deléham, Oct 09 2007

Sum_{k=0..n} T(n,k)*2^k = A062878(n+1)/3. - Philippe Deléham, Aug 31 2009