A258712 Motzkin numbers A001006 read mod 5.

1, 1, 2, 4, 4, 1, 1, 2, 3, 0, 3, 3, 1, 0, 4, 2, 2, 4, 2, 4, 4, 4, 3, 0, 2, 1, 1, 2, 4, 4, 1, 1, 2, 3, 0, 3, 3, 1, 0, 4, 2, 2, 4, 2, 4, 4, 4, 3, 4, 3, 3, 3, 1, 2, 2, 3, 3, 1, 4, 0, 4, 4, 3, 0, 2, 1, 1, 2, 1, 2, 2, 2, 4, 3, 3, 2, 2, 4, 3, 3, 2, 2, 4, 1, 0, 1, 1, 2, 0

Offset: 0

Author

N. J. A. Sloane, Jun 14 2015

Keywords

• nonn

Links

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

Crossrefs

Cf. A001006.

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

Programs

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], 5];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 26 2019 *)

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) % 5) \\ Altug Alkan, Oct 23 2015