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A128937
Triangle formed by reading A039598 mod 2.
3
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
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
KEYWORD
nonn,tabl,easy
AUTHOR
Philippe Deléham, Apr 27 2007, May 02 2007
STATUS
approved