A258711 Motzkin numbers A001006 read mod 7.

1, 1, 2, 4, 2, 0, 2, 1, 1, 2, 4, 2, 6, 3, 3, 3, 6, 5, 6, 5, 1, 0, 0, 0, 0, 0, 1, 6, 5, 5, 3, 6, 3, 5, 5, 2, 2, 4, 1, 4, 4, 0, 1, 1, 2, 4, 2, 0, 2, 1, 1, 2, 4, 2, 0, 2, 1, 1, 2, 4, 2, 6, 3, 3, 3, 6, 5, 6, 5, 1, 0, 0, 0, 0, 0, 1, 6, 5, 5, 3, 6, 3, 5, 5, 2, 2, 4, 1, 4

Offset: 0

Author

N. J. A. Sloane, Jun 14 2015

Keywords

• nonn

Links

• Rob Burns, Structure and asymptotics for Motzkin numbers modulo small primes using automata, arXiv:1612.08146 [math.NT], 2016.
• 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

m[0] = 1; m[n_] := m[n] = m[n-1] + Sum[m[k] m[n-k-2], {k, 0, n-2}];
a[n_] := Mod[m[n], 7];
Array[a, 100, 0] (* Jean-François Alcover, Nov 05 2018 *)

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