A327134 - OEIS

%I #13 May 11 2022 15:58:43

%S 0,1,1,1,1,2,3,3,4,7,9,11,14,20,27,34,40,53,68,80,94,121,145,169,197,

%T 236,279,322,362,426,494,555,622,717,810,904,1003,1132,1266,1402,1534,

%U 1712,1898,2073,2256,2497,2733,2969,3215,3515,3825,4135,4440,4826,5222

%N The number of monomials in a strong elliptic divisibility sequence t_n in free variables x, y, z.

%H Clark Kimberling, <a href="http://www.fq.math.ca/Scanned/17-1/kimberling1.pdf">Strong divisibility sequences and some conjectures</a>, Fib. Quart., 17 (1979), 13-17.

%e t_1 = 1, t_2 = x, t_3 = y, t_4 = x*z, a(1) = a(2) = a(3) = a(4) = 1, t_5 = x^4*z - y^3, a(5) = 2. t_6 = x^5*y*z - x*y^4 - x*y*z^2, a(6) = 3. t_7 = x^4*y^3*z - x^4*z^3 - y^6, a(7) = 3.

%t a[ n_] := a[n] = If[ Abs@n <= 4, Boole[n != 0], Length @ t[n]]; t[ n_] := t[n] = Sign[n] If[ Abs@n <= 4, {0, 1, x, y, x z}[[Abs[n] + 1]], (x^2 t[n-1] t[n-3] - y t[n-2]^2) / t[n-4] // Factor // Expand];

%K nonn

%O 0,6

%A _Michael Somos_, Nov 28 2019