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

0,3

Links

Table of n, a(n) for n=0..88.

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

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 *)

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) % 7) \\ 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: A209466 A277659 A331144 * A127278 A378010 A356165

Adjacent sequences: A258708 A258709 A258710 * A258712 A258713 A258714

Keyword

nonn

Author

N. J. A. Sloane, Jun 14 2015

Status

approved