A125046 Partial sums of A003095.

0, 1, 3, 8, 34, 711, 459041, 210066847942, 44127887746116242835744, 1947270476915296449559747573381595046695626949, 3791862310265926082868235028027893277370233154194659061677030600277515827791936222020978975

Offset: 0

Author

Jonathan Vos Post, Jan 08 2007

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..13
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

Cf. A003095, A076949.

Programs

Mathematica

Accumulate[NestList[#^2 + 1 &, 0, 11]] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2012 *)
RecurrenceTable[{a[0]==0, a[1]==1, a[n] == a[n-1]^2 - 2*a[n-1]*a[n-2]+a[n-2]^2 + a[n-1] + 1}, a, {n, 0, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)

PARI

a(n)=if(n>1,a(n-1)^2-2*a(n-1)*a(n-2)+a(n-2)^2+a(n-1)+1,n) \\ Charles R Greathouse IV, Dec 29 2011

Formula

a(n) = a(n-1)^2 - 2a(n-1)a(n-2)+a(n-2)^2 + a(n-1) + 1 for n > 1. [Charles R Greathouse IV, Dec 29 2011]

a(n) ~ c^(2^n), where c = A076949 = 1.225902443528748538627947495913... . - Vaclav Kotesovec, Dec 18 2014