A113848 a(1) = a(2) = 1, a(n+2) = 2*a(n) + a(n+1)^2.

1, 1, 3, 11, 127, 16151, 260855055, 68045359719085327, 4630170979299719971778494028407039, 21438483297549327871400796194793048411084076762817293736211302918175

Offset

1,3

Comments

In this sequence the primes begin a(3) = 3, a(4) = 11, a(5) = 127, a(9) = 4630170979299719971778494028407039.

Links

Table of n, a(n) for n=1..10.

Index entries for sequences of form a(n+1)=a(n)^2 + ...

Formula

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

a(n) ~ c^(2^n), where c = 1.163464453662702696843453679269882816346479873363677551158525103156732040997... . - Vaclav Kotesovec, Dec 18 2014

Example

a(1) = 1 by definition.
a(2) = 1 by definition.
a(3) = 2*1 + 1^2 = 3.
a(4) = 2*1 + 3^2 = 11.
a(5) = 2*3 + 11^2 = 127.
a(6) = 2*11 + 127^2 = 16151.

Mathematica

Join[{a=1, b=1}, Table[c=1*b^2+2*a; a=b; b=c, {n, 10}]] (* Vladimir Joseph Stephan Orlovsky, Jan 18 2011 *)
RecurrenceTable[{a[1]==1, a[2]==1, a[n] == 2*a[n-2] + a[n-1]^2}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)

Crossrefs

Cf. A000278, A000283, A014253, A063827, A072878, A112957, A112958, A112959, A112960, A112961, A112969, A113785.

Sequence in context: A339326 A102847 A113258 * A287429 A274664 A219620

Adjacent sequences: A113845 A113846 A113847 * A113849 A113850 A113851

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 24 2006

Status

approved