A118112 a(n) = binomial(3n,n) mod (n+1).

1, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 19, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 35, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,5

Comments

These divisibilities are analogous to those of Catalan numbers. For rather long sequences of consecutive integers, a(n)=0. For the first 10000 integers 9678 residues equals zero. See A118113.

If n+1 is in A061345, a(n)=0. This follows from Kummer's theorem. - Robert Israel, May 09 2018

Links

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

Wikipedia, Kummer's theorem

Formula

a(n) = binomial(3n,n) mod (n+1).

Example

For n=9, binomial(27,7) = 4686825; 4686825 mod 10 = 5.

Maple

seq(binomial(3*n, n) mod (n+1), n=1..200); # Robert Israel, May 09 2018

Mathematica

Table[Mod[Binomial[3*k, k], k+1], {k, 500}]

Prog

(PARI) a(n) = binomial(3*n, n) % (n+1); \\ Michel Marcus, May 10 2018

Crossrefs

Cf. A000108, A061345, A118113.

Sequence in context: A096133 A349379 A293381 * A245552 A195938 A184762

Adjacent sequences: A118109 A118110 A118111 * A118113 A118114 A118115

Keyword

nonn

Author

Labos Elemer, Apr 13 2006

Extensions

Mathematica program corrected by Harvey P. Dale, Dec 28 2012

Status

approved