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

1,2

Comments

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

Links

Table of n, a(n) for n=1..48.

Formula

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

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 *)

Crossrefs

Cf. A066796, A083097, A081601.

Sequence in context: A334587 A329947 A115912 * A307348 A289691 A145469

Adjacent sequences: A083093 A083094 A083095 * A083097 A083098 A083099

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 22 2003

Status

approved