A137992 A014137 (= partial sums of Catalan numbers A000108) mod 3.

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

Offset: 0

Author

M. F. Hasler, Mar 16 2008

Keywords

• easy
• nonn

Comments

As usual, "mod 3" means to choose the unique representative in { 0,1,2 } of the equivalence class modulo 3Z.

Crossrefs

Cf. A014137, A000108, A137821-A137824, A107755; A014138(n)+1 = a(n+1) (mod 3).

Programs

PARI

A137992(n) = lift( sum( k=0,n, binomial( 2*k,k )/(k+1), Mod(0,3) ))

Formula

a(n) = sum( k=0..n, C(k) ) (mod 3), where C(k) = binomial(2k,k)/(k+1).

a(n) = 1 <=> n = 2 A137821(m) for some m (with A137821(0)=0).