A299919 Motzkin numbers (A001006) mod 4.

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

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Maple

f:= rectoproc({(3+3*n)*a(n)+(5+2*n)*a(1+n)+(-4-n)*a(n+2), a(0) = 1, a(1) = 1}, a(n), remember):
seq(f(n) mod 4, n=0..200); # Robert Israel, Mar 16 2018

Mathematica

b = DifferenceRoot[Function[{b, n}, {3(n+1) b[n] + (2n+5) b[n+1] == (n+4) b[n+2], b[0] == 1, b[1] == 1}]];
a[n_] := Mod[b[n], 4];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 26 2019 *)

Crossrefs

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

Sequence in context: A246181 A123226 A347382 * A238270 A292521 A350828

Adjacent sequences: A299916 A299917 A299918 * A299920 A299921 A299922

Keyword

nonn

Author

N. J. A. Sloane, Mar 16 2018

Status

approved