A179554 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.

1, 1, 1, 1, 1, 1, 2, 5, 29, 1241, 3642581, 80305336110269, 93845241317908146817718208193, 1831028415236189172750287983272896126569309241020364043033034

Offset: 1

Author

Michael Somos, Jan 08 2011

Keywords

• nonn

Comments

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

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.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..17
• A. P. Fordy and R. J. Marsh, Cluster Mutation-Periodic Quivers and Associated Laurent Sequences, arXiv:0904.0200 [math.CO], 2009-2011.
• A. N. W. Hone, Laurent Polynomials and Superintegrable Maps, arXiv:math/0702280 [math.NT], 2007.

Programs

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

Mathematica

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

Formula

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