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

0,1

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.

Links

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

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).

Example

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;

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 *)

Prog

(Magma) [(Catalan(n-k+1) mod 2): k in [0..n], n in [0..15]]; // 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

Crossrefs

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

Sequence in context: A294878 A023960 A129686 * A266719 A024711 A286990

Adjacent sequences: A104971 A104972 A104973 * A104975 A104976 A104977

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 30 2005

Status

approved