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A299919 Motzkin numbers (A001006) mod 4.

%I A299919 #14 Feb 26 2019 19:11:48
%S A299919 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,
%T A299919 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,
%U A299919 3,3,1,1,1,1,0,2,1,1,2,0,1,1,2,0,1
%N A299919 Motzkin numbers (A001006) mod 4.
%H A299919 Robert Israel, <a href="/A299919/b299919.txt">Table of n, a(n) for n = 0..10000</a>
%p A299919 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):
%p A299919 seq(f(n) mod 4, n=0..200); # _Robert Israel_, Mar 16 2018
%t A299919 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}]];
%t A299919 a[n_] := Mod[b[n], 4];
%t A299919 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Feb 26 2019 *)
%Y A299919 Motzkin numbers A001006 read mod 2,3,4,5,6,7,8,11: A039963, A039964, A299919, A258712, A299920, A258711, A299918, A258710.
%K A299919 nonn
%O A299919 0,3
%A A299919 _N. J. A. Sloane_, Mar 16 2018