A113848 - OEIS (original) (raw)

A113848

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

1

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

COMMENTS

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

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

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.