Search: id:A002814
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%I A002814 M2105 N0833
%S A002814 1,2,17,5777,192900153617,7177905237579946589743592924684177,
%T A002814 369822356418414944143680173221426891716916679027557977938929258031490127514207143830378340325399155217
%N A002814 a(n) = a(n-1)^3 + 3a(n-1)^2 - 3.
%C A002814 An infinite coprime sequence defined by recursion. - Michael Somos Mar 
               14 2004
%D A002814 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002814 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002814 L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 
               256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see 
               vol. 1, p. 397.
%D A002814 E. Lucas, Nouveaux theoremes d'arithmetique superieure, Comptes Rend., 
               83 (1876), 1286-1288.
%D A002814 M. Mendes France and A. J. van der Poorten, From geometry to Euler identities, 
               Theoret. Comput. Sci., 65 (1989), 213-220.
%D A002814 J. O. Shallit, Predictable regular continued cotangent expansions. J. 
               Res. Nat. Bur. Standards Sect. B 80B (1976), no. 2, 285-290.
%F A002814 a(n) = Fib(3^n)/Fib(3^(n-1)) - Henry Bottomley (se16(AT)btinternet.com), 
               Jul 10 2001
%F A002814 a(n+1) = 5*(f(n))^2 - 3, where f(n) = Fib(3^n) = product of first n entries. 
               - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 16 2003
%F A002814 Contribution from Artur Jasinski (grafix(AT)csl.pl), Oct 05 2008: (Start)
%F A002814 a(n+2)=(G^(3^(n + 1)) - (1 - G)^(3^(n + 1)))/((G^(3^n)) - (1 - G)^(3^n)) 
               where G = (1 + Sqrt[5])/2
%F A002814 a(n+2)=A045529(n+1)/A045529(n) (End)
%t A002814 G = (1 + Sqrt[5])/2; Table[Expand[(G^(3^(n + 1)) - (1 - G)^(3^(n + 1)))/
               Sqrt[5]]/Expand[((G^(3^n)) - (1 - G)^(3^n))/Sqrt[5]], {n, 1, 7}] 
               [From Artur Jasinski (grafix(AT)csl.pl), Oct 05 2008]
%o A002814 (PARI) a(n)=if(n<2,max(0,n+1),a(n-1)^3+3*a(n-1)^2-3)
%Y A002814 Cf. A000045, A001566.
%Y A002814 Cf. A045529.
%Y A002814 Sequence in context: A122054 A092415 A060353 this_sequence A122207 A003819 
               A078624
%Y A002814 Adjacent sequences: A002811 A002812 A002813 this_sequence A002815 A002816 
               A002817
%K A002814 nonn,easy,nice
%O A002814 0,2
%A A002814 N. J. A. Sloane (njas(AT)research.att.com).

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