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A137992
A014137 (= partial sums of Catalan numbers A000108) mod 3.
2
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
0,2
COMMENTS
As usual, "mod 3" means to choose the unique representative in { 0,1,2 } of the equivalence class modulo 3Z.
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).
PROG
(PARI) A137992(n) = lift( sum( k=0, n, binomial( 2*k, k )/(k+1), Mod(0, 3) ))
CROSSREFS
Cf. A014137, A000108, A137821-A137824, A107755; A014138(n)+1 = a(n+1) (mod 3).
Sequence in context: A307332 A275409 A029343 * A047654 A358477 A351981
KEYWORD
easy,nonn
AUTHOR
M. F. Hasler, Mar 16 2008
STATUS
approved