Search: id:A102446
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%I A102446
%S A102446 2,2,10,18,58,130,362,882,2330,5858,15178,38610,99322,253762,651050,
%T A102446 1666098,4270298,10934690,28015882,71754642,183818170,470836738,
%U A102446 1206109418,3089456370,7913894042,20271719522,51927295690,133014173778
%N A102446 a(n) = a(n-1) + 4*a(n-2), a(0) = a(1) = 2.
%C A102446 The continued fraction expansion c_0 = 0, c_n = 1/2 (n>0) (see a paper 
               by Bremner & Tzanakis) has convergents 2/1, 2/5, 10/9, 18/29, 58/
               65, 130/181, ... where the numerators and denominators satisfy the 
               recurrence a_n = a_{n-1} + 4a_{n-2}. The denominators are A006131 
               and the numerators are the present sequence.
%t A102446 a[0] = a[1] = 2; a[n_] := a[n] = a[n - 1] + 4a[n - 2]; Table[ a[n], {n, 
               0, 27}] (from Robert G. Wilson v Feb 23 2005)
%o A102446 sage: from sage.combinat.sloane_functions import recur_gen2b sage: it 
               = recur_gen2b(2,2,1,4, lambda n: 0) sage: [it.next() for i in range(29)] 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2008
%Y A102446 Equals 2*A006131(n).
%Y A102446 Sequence in context: A015623 A164124 A003609 this_sequence A151456 A151389 
               A151428
%Y A102446 Adjacent sequences: A102443 A102444 A102445 this_sequence A102447 A102448 
               A102449
%K A102446 nonn,easy
%O A102446 0,1
%A A102446 N. J. A. Sloane (njas(AT)research.att.com), based on a suggestion from 
               R. K. Guy, Feb 23 2005
%E A102446 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 23 2005

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