A127872 Triangle formed by reading A039599 mod 2.

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

Offset: 0

Author

Philippe Deléham, Apr 05 2007

Keywords

• nonn
• tabl

Comments

Also triangle formed by reading triangles A061554, A106180, A110519, A124574, A124576, A126953, A127543 modulo 2.

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A061554, A106180, A110519, A124574, A124576, A126953, A127543.

Cf. A000007, A036987, A001316, A062878, A050614, A000045, A001519

Programs

Mathematica

T[0, 0] := 1; T[n_, k_] := Binomial[2*n - 1, n - k] - Binomial[2*n - 1, n - k - 2]; Table[Mod[T[n, k], 2], {n,0,10}, {k,0,n}] // Flatten (* G. C. Greubel, Apr 18 2017 *)

Formula

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A036987(n), A001316(n), A062878(n) for x=-1,0,1,2 respectively.

Sum_{k=0..n} T(n,k)*Fibonacci(2*k+1) = A050614(n), see A000045 and A001519. - Philippe Deléham, Aug 30 2007