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a(n) = a(n-1)*a(n-2) + 1, with a(0) = a(1) = 2.
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%I #24 Sep 08 2022 08:46:14

%S 2,2,5,11,56,617,34553,21319202,736642386707,15704627843968647815,

%T 11568694537326272321321120595206,

%U 181682042349262169758803442669575561298555791374891,2101824050856189730969091901210449068013789839106586804501928241686514359003372547

%N a(n) = a(n-1)*a(n-2) + 1, with a(0) = a(1) = 2.

%H G. C. Greubel, <a href="/A262714/b262714.txt">Table of n, a(n) for n = 0..17</a>

%t RecurrenceTable[{a[0]==a[1]==2, a[n]==a[n-1]*a[n-2] +1}, a, {n, 0, 20}]

%o (Magma) [n le 2 select 2 else Self(n-1)*Self(n-2)+1: n in [1..20]];

%o (PARI) a(n) = if(n<2, 2, 1 + a(n-1)*a(n-2))

%o vector(20, n, a(n-1)) \\ _Altug Alkan_, Sep 30 2015

%o (PARI) {a(n) = if( n<2, 2 * (n>=0), self()(n-1) * self()(n-2) + 1)}; /* _Michael Somos_, Oct 02 2015 */

%o (Sage)

%o def a(n):

%o if (n==0 or n==1): return 2

%o else: return a(n-1)*a(n-2) +1

%o [a(n) for n in (0..20)] # _G. C. Greubel_, Jun 07 2019

%Y Cf. A007660, A055937.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Sep 30 2015