A165896 a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)+a(n-1)*a(n-3)+a(n-2)*a(n-3))/a(n-4) with four initial ones.

1, 1, 1, 1, 6, 51, 3001, 9180001, 14050074147451, 3870680638643416483474006, 4992392071450646411005278674572370014340582601, 2715030052293379508289500941366397276374058263752394148988972928520177978202810359001

Offset: 0

Author

Jaume Oliver Lafont, Sep 29 2009

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..15
• S. Fomin, A. Zelevinsky, The Laurent Phenomenon, Adv. Appl. Math. 28 (2) (2002) 119-144. [_R. J. Mathar_, Oct 23 2009]
• Sergey Fomin, Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241 [math.CO], 2001. [_R. J. Mathar_, Oct 23 2009]

Crossrefs

Cf. A006720, A165903.

Programs

Mathematica

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]^2+a[n-2]^2+a[n-3]^2+ a[n-1]a[n-2]+ a[n-1]a[n-3]+a[n-2]a[n-3])/a[n-4]},a,{n,13}] (* Harvey P. Dale, May 21 2012 *)

PARI

a(n)=if(n<4,1,(a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)+a(n-1)*a(n-3)+a(n-2)*a(n-3))/a(n-4))

Formula

a(n) ~ 1/sqrt(10) * c^(t^n), where t = A058265 = 1.8392867552141611325518525646532866..., c = 1.2712241060822553131735186905646486868228186258439... . - Vaclav Kotesovec, May 06 2015

a(n) = 10*a(n-1)*a(n-2)*a(n-3)-a(n-1)-a(n-2)-a(n-3)-a(n-4). - Bruno Langlois, Aug 21 2016