A072458 Shadow transform of Catalan numbers A000108.

0, 1, 0, 0, 0, 1, 1, 2, 0, 0, 1, 4, 1, 5, 4, 1, 0, 7, 2, 8, 3, 3, 7, 10, 2, 3, 9, 0, 5, 13, 9, 14, 0, 6, 12, 4, 3, 17, 14, 8, 4, 19, 8, 20, 9, 8, 19, 22, 1, 8, 6, 10, 12, 25, 6, 11, 11, 15, 25, 28, 14, 29, 28, 10, 0, 10, 15, 32, 19, 22, 17, 34, 11, 35, 32, 15, 22, 17, 21, 38, 3, 0, 36, 40, 19, 21

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..4000

Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform.

N. J. A. Sloane, Transforms.

Maple

a:= n-> add(`if`(modp(binomial(2*j, j)/(j+1), n)=0, 1, 0), j=0..n-1):
seq(a(n), n=0..120);  # Alois P. Heinz, Sep 16 2019

Mathematica

a[n_] := Sum[If[Mod[Binomial[2*j, j]/(j+1), n] == 0, 1, 0], {j, 0, n-1}];
Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Jan 07 2025, after Alois P. Heinz *)

Crossrefs

Cf. A072480.

Sequence in context: A137585 A301344 A301579 * A256282 A258256 A361290

Adjacent sequences: A072455 A072456 A072457 * A072459 A072460 A072461

Keyword

nonn,look

Author

N. J. A. Sloane, Aug 02 2002, corrected Aug 21 2002

Status

approved