A100523 a(n) = a(n-1)^2 + 2*a(n-1) - 1 with a(0) = 1.

1, 2, 7, 62, 3967, 15745022, 247905749270527, 61457260521381894004129398782, 3776994870793005510047522464634252677140721938309041881087

Offset: 0

Author

Reinhard Zumkeller, Nov 24 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..12
• Index entries for sequences of form a(n+1) = a(n)^2 + ...

Crossrefs

Cf. A004019.

Programs

Magma

[n le 1 select 1 else Self(n-1)^2 +2*Self(n-1) -1: n in [1..13]]; // G. C. Greubel, Jun 26 2022

Mathematica

RecurrenceTable[{a[n] == a[n-1]^2 + a[n-1]*2 - 1, a[0] == 1}, a, {n, 0, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
NestList[#^2+2#-1&,1,10] (* Harvey P. Dale, Aug 17 2025 *)

SageMath

def a(n): return 1 if (n==0) else a(n-1)^2 + 2*a(n-1) - 1 # a=A100523
[a(n) for n in (0..12)] # G. C. Greubel, Jun 26 2022

Formula

a(n) ~ c^(2^n), where c = 1.6784589651254290832096890907802189718037513767396728769965837700954845976... . - Vaclav Kotesovec, Dec 18 2014