A242995 - OEIS

%I #28 Sep 08 2022 08:46:08

%S 2,3,5,-11,-779,497941,181860254581,16687694789137362648661,

%T -263439569256003706800705587722279993788907979

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

%H G. C. Greubel, <a href="/A242995/b242995.txt">Table of n, a(n) for n = 1..13</a>

%H M. Chamberland and M. Martelli, <a href="https://chamberland.math.grinnell.edu/papers/mario_digits.pdf">Unbounded Orbits and Binary Digits</a>, Grinnell College.

%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>

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

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

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

%t 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 *)

%o (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))};

%o (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

%Y Cf. A127814, A242996.

%K sign

%O 1,1

%A _Michael Somos_, Aug 17 2014