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a(n) = ( ( a(n-1) * a(n-5) )^2 + ( a(n-2) * a(n-3)^2 * a(n-4) )^2 ) / a(n-6), a(1) = ... = a(6) = 1.
6

%I #15 Sep 08 2022 08:45:54

%S 1,1,1,1,1,1,2,5,29,1241,3642581,80305336110269,

%T 93845241317908146817718208193,

%U 1831028415236189172750287983272896126569309241020364043033034

%N a(n) = ( ( a(n-1) * a(n-5) )^2 + ( a(n-2) * a(n-3)^2 * a(n-4) )^2 ) / a(n-6), a(1) = ... = a(6) = 1.

%C Similar to Somos-6 sequence but the recurrence is not bilinear.

%C log( log( a(n))) ~ n * log(c) where c = 2.0810189966245... is largest root of 0 = x^4 - x^3 - 2*x^2 - x + 1 according to Hone.

%H G. C. Greubel, <a href="/A179554/b179554.txt">Table of n, a(n) for n = 1..17</a>

%H A. P. Fordy and R. J. Marsh, <a href="http://arxiv.org/abs/0904.0200">Cluster Mutation-Periodic Quivers and Associated Laurent Sequences</a>, arXiv:0904.0200 [math.CO], 2009-2011.

%H A. N. W. Hone, <a href="http://arxiv.org/abs/math/0702280">Laurent Polynomials and Superintegrable Maps</a>, arXiv:math/0702280 [math.NT], 2007.

%F a(n) = a(7 - n).

%t a[1] = a[2] = a[3] = a[4] = a[5] = a[6] = 1; a[n_ /; n < 1] := a[7 - n];

%t a[n_ /; n > 6] := a[n] = ((a[n - 1] a[n - 5])^2 + (a[n - 2] a[n - 3]^2 a[n - 4])^2)/ a[n - 6];

%o (Magma) I:=[1,1,1,1,1,1]; [n le 6 select I[n] else ((Self(n-1)*Self(n-5) )^2 + (Self(n-2)*Self(n-3)^2*Self(n-4))^2 )/Self(n-6): n in [1..20]]; // _G. C. Greubel_, Aug 14 2018

%K nonn

%O 1,7

%A _Michael Somos_, Jan 08 2011