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A039967 An example of a d-perfect sequence. 1
1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = a(n-1) if n == 0 or 1 (mod 3). a(n) = 0 if n == 5,6, or 7 (mod 9). - Robert Israel, Sep 20 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

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.

FORMULA

a(n) = ((-1)^(n+1)*A001006(n-1)) mod 3. - Christian G. Bower, Jun 12 2005

a(n) = Catalan number(n) mod 3 = A000108(n) mod 3. - Ilya Gutkovskiy, Sep 18 2015

MAPLE

seq(binomial(2*n, n)/(n+1) mod 3, n = 1 .. 100); # Robert Israel, Sep 20 2015

MATHEMATICA

Table[Mod[CatalanNumber[n], 3], {n, 100}] (* Vincenzo Librandi, Sep 20 2015 *)

PROG

(MAGMA) [Catalan(n) mod 3: n in [1..100]]; // Vincenzo Librandi, Sep 20 2015

(PARI) a(n) = binomial(2*n, n)/(n+1) % 3;

vector(100, n, a(n)) \\ Altug Alkan, Sep 28 2015

CROSSREFS

Cf. A000108, A001006, A067397.

Sequence in context: A028953 A037865 A039969 * A258133 A123186 A127323

Adjacent sequences:  A039964 A039965 A039966 * A039968 A039969 A039970

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Christian G. Bower, Jun 12 2005

STATUS

approved

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Last modified February 20 14:37 EST 2018. Contains 299380 sequences. (Running on oeis4.)