A089119 - OEIS

%I #16 Jan 30 2021 04:12:10

%S 4,5,6,13,14,15,16,17,18,19,20,21,22,23,24,31,32,33,40,41,42,43,44,45,

%T 46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,

%U 69,70,71,72,73,74,75,76,77,78,85,86,87,94,95,96,97,98,99,100,101,102

%N Complement of ((3*A005836) union (3*A005836 - 1) union (3*A005836 - 2)).

%C Numbers k such that the Motzkin number A001006(k) == 0 (mod 3).

%C The asymptotic density of this sequence is 1 (Burns, 2016). - _Amiram Eldar_, Jan 30 2021

%H Amiram Eldar, <a href="/A089119/b089119.txt">Table of n, a(n) for n = 1..10000</a>

%H Rob Burns, <a href="https://arxiv.org/abs/1611.04910">Asymptotic density of Motzkin numbers modulo small primes</a>, arXiv:1611.04910 [math.NT], 2016.

%t (* m = MotzkinNumber *) m[0] = 1; m[n_] := m[n] = m[n - 1] + Sum[m[k]*m[n - 2 - k], {k, 0, n - 2}]; Select[Range[0, 120], Mod[m[#], 3] == 0 &] (* _Jean-François Alcover_, Jul 10 2013 *)

%Y Cf. A001006, A005836.

%K nonn

%O 1,1

%A _Emeric Deutsch_ and _Bruce E. Sagan_, Dec 05 2003

%E Offset corrected by _Amiram Eldar_, Jan 30 2021