A039970 An example of a d-perfect sequence: a(2*n) = 0, a(2*n+1) = Catalan(n) mod 3.

1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions, in Sequences and their Applications, C. Ding, T. Helleseth, and H. Niederreiter, eds., Proceedings of SETA'98 (Singapore, 1998), 308-317, 1999. DOI: 10.1007/978-1-4471-0551-0_23

Crossrefs

Cf. A039969.

Programs

Magma

[n mod 2 eq 0 select 0 else Catalan(Floor((n-1)/2)) mod 3: n in [1..100]]; // G. C. Greubel, Feb 13 2019

Mathematica

Table[If[IntegerQ[n/2], 0, Mod[CatalanNumber[(n-1)/2], 3]], {n, 1, 100}] (* G. C. Greubel, Feb 13 2019 *)

PARI

A039969(n) = ((binomial(2*n, n)/(n+1))%3);
A039970(n) = if(n%2,A039969((n-1)/2),0); \\ Antti Karttunen, Feb 13 2019

Sage

def A039970(n):
    if (mod(n,2)==0):
        return 0
    else:
        return mod(catalan_number((n-1)/2), 3)
[A039970(n) for n in (1..100)] # G. C. Greubel, Feb 13 2019

Formula

a(2*n) = 0, a(2*n+1) = A039969(n). - Christian G. Bower, Jun 12 2005, sign edited because of changed offset of A039969. - Antti Karttunen, Feb 13 2019

Extensions

More terms from Christian G. Bower, Jun 12 2005

Formula added to the name by Antti Karttunen, Feb 13 2019