A089119 Complement of ((3*A005836) union (3*A005836 - 1) union (3*A005836 - 2)).

4, 5, 6, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 85, 86, 87, 94, 95, 96, 97, 98, 99, 100, 101, 102

Offset

1,1

Comments

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

The asymptotic density of this sequence is 1 (Burns, 2016). - Amiram Eldar, Jan 30 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Rob Burns, Asymptotic density of Motzkin numbers modulo small primes, arXiv:1611.04910 [math.NT], 2016.

Mathematica

(* 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 *)

Crossrefs

Cf. A001006, A005836.

Sequence in context: A310571 A280382 A055033 * A063833 A260107 A167434

Adjacent sequences: A089116 A089117 A089118 * A089120 A089121 A089122

Keyword

nonn

Author

Emeric Deutsch and Bruce E. Sagan, Dec 05 2003

Extensions

Offset corrected by Amiram Eldar, Jan 30 2021

Status

approved