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A039964 Motzkin numbers A001006 read mod 3. 11
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
Rob Burns, Asymptotic density of Motzkin numbers modulo small primes, arXiv:1611.04910 [math.NT], 2016.
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-François 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: A103633 A350847 A026821 * A369453 A340655 A035172
KEYWORD
nonn
AUTHOR
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 March 19 02:51 EDT 2024. Contains 370952 sequences. (Running on oeis4.)