A083096 Numbers k such that 3 divides Sum_{j=1..k} binomial(2*j,j).

0, 12, 30, 36, 84, 90, 108, 120, 246, 252, 270, 282, 324, 336, 354, 360, 732, 738, 756, 768, 810, 822, 840, 846, 972, 984, 1002, 1008, 1056, 1062, 1080, 1092, 2190, 2196, 2214, 2226, 2268, 2280, 2298, 2304, 2430, 2442, 2460, 2466, 2514, 2520, 2538, 2550

Offset: 1

Author

Benoit Cloitre, Apr 22 2003

Keywords

• nonn
• easy

Comments

Apparently a(n)/3 (mod 3) = A010060(n-1), the Thue-Morse sequence.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A066796, A083097, A081601.

Programs

Mathematica

Reap[ For[n = 0, n <= 3000, n = n + 3, If[ Divisible[ Sum[ Binomial[2 k, k], {k, 1, n}], 3], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 01 2013 *)
Join[{0},Position[Accumulate[Table[Binomial[2k,k],{k,2600}]],?( Divisible[ #,3]&)]//Flatten] (* _Harvey P. Dale, Mar 14 2020 *)

Formula

It appears that sequence gives k such that the coefficient of x^k equals 1 in Product_{j>=1} 1-x^(3^j).