Search: id:A015459
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%I A015459
%S A015459 0,1,1,3,7,31,143,1135,10287,155567,2789039,82439343,2938415279,
%T A015459 171774189743,12207523172527,1419381685547183,201427441344229551,
%U A015459 46711726513354322095,13247460522448782176431
%N A015459 q-Fibonacci numbers for q=2.
%C A015459 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2009: 
               (Start)
%C A015459 Preface the series with another "1": (1, 1, 1, 3, 7,...a(n)). Then a(n+2) 
               =
%C A015459 (1, 1, 1, 3, 7,...a(n)) dot (equal number of terms in (1, 2, 4, 8,...)).
%C A015459 Example: (143) = (1, 1, 1, 3, 7) dot (1, 2, 4, 8, 16) = (1 + 2 + 4 + 
               24 + 112).
%C A015459 Analogous procedures apply to other q-Fibonacci sequences for q(n). (End)
%F A015459 a(n) = a(n-1) + 2^(n-2) a(n-2).
%F A015459 Associated constant: C_2=lim n ->infty a(n)*a(n-2)/a(n-1)^2 =1.225306147422043724739386133....(C_1=1) 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 30 2003
%Y A015459 Cf. A015460.
%Y A015459 Sequence in context: A121620 A042271 A000644 this_sequence A115083 A141385 
               A059296
%Y A015459 Adjacent sequences: A015456 A015457 A015458 this_sequence A015460 A015461 
               A015462
%K A015459 nonn,easy
%O A015459 0,4
%A A015459 Olivier Gerard (olivier.gerard(AT)gmail.com)

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