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A039964 Motzkin numbers A001006 read mod 3. 9
1, 1, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

An example of a d-perfect sequence.

The asymptotic mean of this sequence is 0 (Burns, 2016). - Amiram Eldar, Jan 30 2021

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000

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

Anders Hyllengren, Letter to N. J. A. Sloane, Oct 04 1985.

David Kohel, San Ling and Chaoping Xing, Explicit Sequence Expansions, in: C. Ding, T. Helleseth and H. Niederreiter (eds.), Sequences and their Applications, Proceedings of SETA'98 (Singapore, 1998), Discrete Mathematics and Theoretical Computer Science, 1999, pp. 308-317; alternative link.

FORMULA

a(n) = A001006(n) mod 3. - Christian G. Bower, Jun 12 2005

MATHEMATICA

b = DifferenceRoot[Function[{b, n}, {3 (n + 1) b[n] + (2 n + 5) b[n + 1] == (n + 4) b[n + 2], b[0] == 1, b[1] == 1}]];

a[n_] := Mod[b[n], 3];

Table[a[n], {n, 0, 104}] (* Jean-Fran├žois Alcover, Feb 26 2019 *)

PROG

(PARI) a001006(n) = polcoeff((1-x-sqrt((1-x)^2-4*x^2+x^3*O(x^n)))/(2*x^2), n);

vector(200, n, n--; a001006(n) % 3) \\ Altug Alkan, Oct 23 2015

CROSSREFS

Cf. A001006.

Motzkin numbers A001006 read mod 2,3,4,5,6,7,8,11: A039963, A039964, A299919, A258712, A299920, A258711, A299918, A258710.

Sequence in context: A280456 A103633 A026821 * A340655 A035172 A110174

Adjacent sequences:  A039961 A039962 A039963 * A039965 A039966 A039967

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Christian G. Bower, Jun 12 2005

Offset adapted by Altug Alkan, Oct 23 2015

STATUS

approved

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Last modified April 14 07:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)