A039971 An example of a d-perfect sequence.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• 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

Programs

Magma

[Binomial(n, Floor(n/2)) mod 3: n in [0..140]]; // Vincenzo Librandi, Jul 20 2016

Mathematica

Table[Mod[Binomial[n - 1, Floor[(n - 1)/2]], 3], {n, 120}] (* or *)
Table[Function[n, Mod[-(-1)^(n + 1) Sum[Binomial[n, k] CatalanNumber@ k, {k, 0, n}], 3]][n - 1], {n, 120}] (* Michael De Vlieger, Jul 19 2016 *)

Formula

a(n) = ((-1)^(n+1)*A007317(n)) mod 3 - Christian G. Bower, Jun 12 2005

a(n) = A001405(n-1) mod 3. - John M. Campbell, Jul 19 2016

Extensions

More terms from Christian G. Bower, Jun 12 2005