A242996 a(n) = (a(n-1)^2 - a(n-2)^4) * a(n-1) / a(n-2)^2 with a(1) = 1, a(2) = 2.

1, 2, 6, 30, -330, 257070, 128005692870, 23279147893155496537470, 388475314992168993748220639081347493631827670

Offset: 1

Author

Michael Somos, Aug 17 2014

Keywords

• sign

Comments

The next term (a(10)) has 90 digits and a(11) has 178 digits. - Harvey P. Dale, Feb 23 2023

Links

• G. C. Greubel, Table of n, a(n) for n = 1..13

Crossrefs

Cf. A127815, A242995.

Programs

Magma

I:=[1,2]; [n le 2 select I[n] else (Self(n-1)^2 - Self(n-2)^2 )/Self(n-2)^2: n in [1..10]]; // G. C. Greubel, Aug 06 2018

Mathematica

RecurrenceTable[{a[n] == (a[n-1]^2 - a[n-2]^4)*a[n-1]/a[n-2]^2, a[1] == 1, a[2] == 2}, a, {n, 1, 10}] (* G. C. Greubel, Aug 06 2018; corrected by Georg Fischer, Dec 07 2023 *)
nxt[{a_,b_}]:={b,(b^2-a^4) b/a^2}; NestList[nxt,{1,2},10][[;;,1]] (* Harvey P. Dale, Feb 23 2023 *)

PARI

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

Formula

abs(a(n)) = A127815(n).

a(n+1) = a(n) * A242995(n) for all n>0.

0 = a(n)^2*a(n+2) + a(n+1)*(a(n)^4 - a(n+1)^2) for all n>0.