A242995 a(n) = a(n-1)^2 + a(n-1)*a(n-2)^2 - a(n-2)^4 with a(1) = 2, a(2) = 3.

2, 3, 5, -11, -779, 497941, 181860254581, 16687694789137362648661, -263439569256003706800705587722279993788907979

Offset: 1

Author

Michael Somos, Aug 17 2014

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 1..13
• M. Chamberland and M. Martelli, Unbounded Orbits and Binary Digits, Grinnell College.
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

Cf. A127814, A242996.

Programs

Magma

I:=[2,3]; [n le 2 select I[n] else Self(n-1)^2 + Self(n-1)*Self(n-2)^2 - Self(n-2)^4: n in [1..10]]; // G. C. Greubel, Aug 05 2018

Mathematica

RecurrenceTable[{a[n] == a[n-1]^2 + a[n-1]*a[n-2]^2 - a[n-2]^4, a[1] == 2, a[2] == 3}, a, {n, 1, 10}] (* G. C. Greubel, Aug 05 2018 *)

PARI

{a(n) = if( n<1, 0, if( n<3, n+1, my(x = a(n-2)^2, y = a(n-1)); y^2 + x*y - x^2))};

Formula

0 = a(n)^2*(a(n+1) - a(n)^2) - (a(n+2) - a(n+1)^2) for all n>0.

abs(a(n)) = abs(A127814(n)) for all n>0.

a(n) = A242996(n+1) / A242996(n) for all n>0.