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%I #7 Mar 14 2020 03:14:24
%S 1,1,1,1,1,2,3,4,7,11,16,23,33,46,64,84,109,143,184,228,283,351,429,
%T 515,615,734,871,1017,1181,1376,1593,1821,2077,2372,2694,3035,3409,
%U 3832,4294,4777,5299,5888,6522,7180,7891,8681,9523,10400,11337,12367,13465
%N Number of terms in polynomial sequence s(n) = (x*s(n-1)*s(n-4) + y*s(n-2)*s(n-3))/s(n-5), with s(k) = 1 for k = 0..4.
%C s(n) is a generalized Somos-5 sequence (A006721) having coefficients x, y in the recurrence numerator sum of products.
%F a(n) = a(4-n) for all n in Z.
%e a(7) = 4 because s(7) = x^3 + x^2*y + 2*x*y*z + y^2*z has 4 terms.
%t a[ n_] := If[0 <= n <= 4, 1, RecurrenceTable[{s[m]*s[m - 5] == x*s[m - 1]*s[m - 4] + y*s[m - 2]*s[m - 3], s[0] == s[1] == s[2] == s[3] == s[4] == 1}, s, {m, Max[n, 4 - n]}] // Last // Factor // Expand // Length];
%Y Cf. A006721.
%K nonn
%O 0,6
%A _Michael Somos_, Mar 13 2020
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