Search: id:A062114
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%I A062114
%S A062114 0,1,2,3,6,9,16,25,42,67,110,177,288,465,754,1219,1974,3193,5168,8361,
%T A062114 13530,21891,35422,57313,92736,150049,242786,392835,635622,1028457,
%U A062114 1664080,2692537,4356618,7049155,11405774,18454929,29860704,48315633
%N A062114 2*Fibonacci(n) - [1 - (-1)^n]/2.
%H A062114 Harry J. Smith, <a href="b062114.txt">Table of n, a(n) for n=0,...,400</
               a>
%F A062114 A bistable recurrence; Fibonacci with a grain of salt: a(0)=0; a(1)=1; 
               a(n)=a(n-1)+a(n-2)+(1+(-1)^n)/2.
%F A062114 a(n+1)=sum(k=0, n, binomial(n-floor(k/2), floor(k/2))) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), May 05 2005
%F A062114 Starting with 1, equals row sums of triangle A134513. - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Oct 28 2007
%F A062114 a(n)=(1/2)*[(-1)^n-1]+(2/5)*sqrt(5)*{[(1/2)+(1/2)*sqrt(5)]^n-[(1/2)-(1/
               2)*sqrt(5)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Jan 
               13 2009]
%e A062114 a(4)= a(3) + a(2) + (1+1)/2 = 3 + 2 + 1 = 6.
%o A062114 (PARI) { h=-1; g=1; for (n=0, 400, f=g + h; h=g; g=f; write("b062114.txt", 
               n, " ", 2*f - (1 - (-1)^n)/2) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Aug 01 2009]
%Y A062114 Cf. A052952, A134513.
%Y A062114 Sequence in context: A147063 A007865 A052812 this_sequence A094768 A093830 
               A118033
%Y A062114 Adjacent sequences: A062111 A062112 A062113 this_sequence A062115 A062116 
               A062117
%K A062114 easy,nonn
%O A062114 0,3
%A A062114 Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 05 2001
%E A062114 Definition corrected by Harry J. Smith, Aug 01 2009

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