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

1,5

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

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A039969.

Sequence in context: A038555 A138108 A158777 * A179212 A105118 A245359

Adjacent sequences: A039967 A039968 A039969 * A039971 A039972 A039973

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Christian G. Bower, Jun 12 2005

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

Status

approved