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A338218 Number of terms in polynomial sequence s(n) = x*y*z*(s(n-1)*s(n-3) + s(n-2)^2)/s(n-4), with s(1) = x, s(2) = s(3) = 1, s(4) = y.

%I A338218 #11 Feb 14 2021 13:16:00
%S A338218 1,1,1,1,2,3,6,12,23,43,80,140,233,387,612,930,1411,2067,2936,4170,
%T A338218 5768,7796,10537,13960,18163,23639,30285,38249,48322,60285,74340,
%U A338218 91706,111967,135403
%N A338218 Number of terms in polynomial sequence s(n) = x*y*z*(s(n-1)*s(n-3) + s(n-2)^2)/s(n-4), with s(1) = x, s(2) = s(3) = 1, s(4) = y.
%C A338218 The Somos-4 polynomial sequence is s(n).
%H A338218 Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/somospol.html">Somos polynomials</a>
%F A338218 a(n) = a(5-n) for all n in Z.
%e A338218 a(6) = 3 because s(6) = x*y^3*z^2 + x*y^3*z + x*y^2*z^2 has 3 terms.
%t A338218 a[ n_] := If[1 <= n <= 4, 1, RecurrenceTable[{s[m]*s[m - 4] == x*y*z*(s[m - 1]*s[m - 3] + s[m - 2]^2), s[1] == x, s[2] == 1, s[3] == 1, s[4] == y}, s, {m, Max[n, 5 - n]}] // Last // Factor // Expand // Length];
%Y A338218 Cf. A333260.
%K A338218 nonn,more
%O A338218 1,5
%A A338218 _Michael Somos_, Jan 29 2021
%E A338218 a(31)-a(34) from _Jinyuan Wang_, Feb 14 2021