A104974 A Fredholm-Rueppel triangle.

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

Offset: 0

Author

Paul Barry, Mar 30 2005

Keywords

• easy
• nonn
• tabl

Comments

Sequence matrix for A036987(n+1).

Riordan array ( (Sum_{k>=0} x^(2^k)/x^2) - 1/x, x).

Diagonal sums are A070939(n+1), with interpolated zeros.

Inverse is A104975.

Examples

			Triangle begins as:
  1;
  0, 1;
  1, 0, 1;
  0, 1, 0, 1;
  0, 0, 1, 0, 1;
  0, 0, 0, 1, 0, 1;
  1, 0, 0, 0, 1, 0, 1;
  0, 1, 0, 0, 0, 1, 0, 1;
  0, 0, 1, 0, 0, 0, 1, 0, 1;
  0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
  0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
  0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
  0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
  0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A000523 (row sums), A036987, A070939, A104975.

Programs

Magma

[(Catalan(n-k+1) mod 2): k in [0..n], n in [0..15]]; // G. C. Greubel, Jun 08 2021

Maple

A104974 := proc(n,k)
    modp(A000108(n+1-k),2);
end proc:
seq(seq( A104974(n,k), k=0..n), n=0..15); # R. J. Mathar, Apr 21 2021

Mathematica

Table[Mod[CatalanNumber[n-k+1], 2], {n,0,15}, {k,0,n}]//Flatten (* G. C. Greubel, Jun 08 2021 *)

Sage

flatten([[mod(catalan_number(n-k+1), 2) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Jun 08 2021

Formula

T(n, k) = A000108(n+1-k) mod 2. [Corrected by R. J. Mathar, Apr 21 2021]

Sum_{k=0..n} T(n, k) = A000523(n+1).