A253853 a(n) = 1 + a(n-2)*a(n-3), with a(0) = a(1) = a(2) = 1.

1, 1, 1, 2, 2, 3, 5, 7, 16, 36, 113, 577, 4069, 65202, 2347814, 265306939, 153082168429, 622891345681347, 40613761521380428832, 95353557892558423217593864, 25297960567233966143149250083396705, 3872666660463510383775257066365338059531886849

Offset: 0

Author

Michael Somos, Jan 17 2015

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..31

Crossrefs

Cf. A007660.

Programs

Haskell

a253853 n = a253853_list !! n
a253853_list = 1 : 1 : 1 : map (+ 1)
                           (zipWith (*) a253853_list $ tail a253853_list)
-- Reinhard Zumkeller, Jan 17 2015

Magma

I:=[1,1,1]; [n le 3 select I[n] else 1 + Self(n-2)*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jan 22 2015

Mathematica

RecurrenceTable[{a[n]==1+a[n-2]*a[n-3],a[0]==1,a[1]==1,a[2]==1},a,{n,0,20}] (* Vaclav Kotesovec, Jan 17 2015 *)

PARI

{a(n) = if( n<3, n>=0, 1 + a(n-2)*a(n-3))};

Formula

a(n+5) == a(n) (mod 2) for all n>=0.

a(n+7) == a(n) (mod 7) for all n>=7.

a(n) ~ c^(d^n), where c = 1.33114442478885300080049... and d = ((27 - 3*sqrt(69)) / 2)^(1/3) / 3 + ((9 + sqrt(69))/2)^(1/3) / 3^(2/3) = 1.324717957244746... is the root of the equation d^3 = d + 1. - Vaclav Kotesovec, Jan 17 2015