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

0,1

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

Links

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

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

Example

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; ...

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

Crossrefs

Cf. A048896 (row sums).

Sequence in context: A127253 A117944 A117945 * A288004 A102511 A266669

Adjacent sequences: A128934 A128935 A128936 * A128938 A128939 A128940

Keyword

nonn,tabl,easy

Author

Philippe Deléham, Apr 27 2007, May 02 2007

Status

approved