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%I #24 Feb 26 2019 19:11:37
%S 1,1,2,4,4,1,1,2,3,0,3,3,1,0,4,2,2,4,2,4,4,4,3,0,2,1,1,2,4,4,1,1,2,3,
%T 0,3,3,1,0,4,2,2,4,2,4,4,4,3,4,3,3,3,1,2,2,3,3,1,4,0,4,4,3,0,2,1,1,2,
%U 1,2,2,2,4,3,3,2,2,4,3,3,2,2,4,1,0,1,1,2,0
%N Motzkin numbers A001006 read mod 5.
%H Anders Hyllengren, <a href="/A258710/a258710.pdf">Letter to N. J. A. Sloane, Oct 04 1985</a>
%t 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 a[n_] := Mod[b[n], 5];
%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Feb 26 2019 *)
%o (PARI) a001006(n) = polcoeff((1-x-sqrt((1-x)^2-4*x^2+x^3*O(x^n)))/(2*x^2), n);
%o vector(200, n, n--; a001006(n) % 5) \\ _Altug Alkan_, Oct 23 2015
%Y Cf. A001006.
%Y Motzkin numbers A001006 read mod 2,3,4,5,6,7,8,11: A039963, A039964, A299919, A258712, A299920, A258711, A299918, A258710.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jun 14 2015
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