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A299920 Motzkin numbers (A001006) mod 6.

%I A299920 #12 Feb 26 2019 19:11:57
%S A299920 1,1,2,4,3,3,3,1,5,1,4,2,1,3,0,0,3,3,0,0,3,3,3,3,3,1,2,4,1,5,1,3,3,3,
%T A299920 4,2,1,1,5,1,3,3,0,0,3,3,0,0,3,3,0,0,3,3,3,3,3,3,0,0,3,3,0,0,3,3,0,0,
%U A299920 3,3,3,3,3,3,0,0,3,3,0,4,5,1,4,2,1,3
%N A299920 Motzkin numbers (A001006) mod 6.
%H A299920 Seiichi Manyama, <a href="/A299920/b299920.txt">Table of n, a(n) for n = 0..10000</a>
%p A299920 f:= gfun:-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 A299920 seq(f(n) mod 6, n=0..100); # _Robert Israel_, Mar 16 2018
%t A299920 b = DifferenceRoot[Function[{b, n}, {3 (n + 1) b[n] + (2 n + 5) b[n + 1] == (n + 4) b[n + 2], b[0] == 1, b[1] == 1}]];
%t A299920 a[n_] := Mod[b[n], 6];
%t A299920 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Feb 26 2019 *)
%Y A299920 Motzkin numbers A001006 read mod 2,3,4,5,6,7,8,11: A039963, A039964, A299919, A258712, A299920, A258711, A299918, A258710.
%K A299920 nonn
%O A299920 0,3
%A A299920 _N. J. A. Sloane_, Mar 16 2018