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

%I A253853 #14 Sep 08 2022 08:46:11
%S A253853 1,1,1,2,2,3,5,7,16,36,113,577,4069,65202,2347814,265306939,
%T A253853 153082168429,622891345681347,40613761521380428832,
%U A253853 95353557892558423217593864,25297960567233966143149250083396705,3872666660463510383775257066365338059531886849
%N A253853 a(n) = 1 + a(n-2)*a(n-3), with a(0) = a(1) = a(2) = 1.
%H A253853 Reinhard Zumkeller, <a href="/A253853/b253853.txt">Table of n, a(n) for n = 0..31</a>
%F A253853 a(n+5) == a(n) (mod 2) for all n>=0.
%F A253853 a(n+7) == a(n) (mod 7) for all n>=7.
%F A253853 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
%t A253853 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 *)
%o A253853 (PARI) {a(n) = if( n<3, n>=0, 1 + a(n-2)*a(n-3))};
%o A253853 (Haskell)
%o A253853 a253853 n = a253853_list !! n
%o A253853 a253853_list = 1 : 1 : 1 : map (+ 1)
%o A253853                            (zipWith (*) a253853_list $ tail a253853_list)
%o A253853 -- _Reinhard Zumkeller_, Jan 17 2015
%o A253853 (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
%Y A253853 Cf. A007660.
%K A253853 nonn
%O A253853 0,4
%A A253853 _Michael Somos_, Jan 17 2015