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

Author

N. J. A. Sloane, Mar 16 2018

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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 *)