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A062114
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2*Fibonacci(n) - [1 - (-1)^n]/2.
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8
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0, 1, 2, 3, 6, 9, 16, 25, 42, 67, 110, 177, 288, 465, 754, 1219, 1974, 3193, 5168, 8361, 13530, 21891, 35422, 57313, 92736, 150049, 242786, 392835, 635622, 1028457, 1664080, 2692537, 4356618, 7049155, 11405774, 18454929, 29860704, 48315633
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,400
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FORMULA
| 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.
a(n+1)=sum(k=0, n, binomial(n-floor(k/2), floor(k/2))) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 05 2005
Starting with 1, equals row sums of triangle A134513. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 28 2007
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 (paoloplava(AT)gmail.com), Jan 13 2009]
a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(n)=a(n-1)+2*a(n-2)-a(n-3)-a(n-4) [From Harvey P. Dale, Nov 02 2011]
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EXAMPLE
| a(4)= a(3) + a(2) + (1+1)/2 = 3 + 2 + 1 = 6.
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MATHEMATICA
| Join[{a=0, b=1}, Table[If[EvenQ[a], c=a+b+1, c=a+b]; a=b; b=c, {n, 0, 5!}]](*From Vladimir Joseph Stephan Orlovsky, Jan 10 2011*)
Table[2Fibonacci[n]-(1-(-1)^n)/2, {n, 0, 40}] (* or *) LinearRecurrence[ {1, 2, -1, -1}, {0, 1, 2, 3}, 41] (* From Harvey P. Dale, Nov 02 2011 *)
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PROG
| (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]
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CROSSREFS
| Cf. A052952, A134513.
Sequence in context: A147063 A007865 A052812 * A094768 A093830 A118033
Adjacent sequences: A062111 A062112 A062113 * A062115 A062116 A062117
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KEYWORD
| easy,nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 05 2001
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EXTENSIONS
| Definition corrected by Harry J. Smith, Aug 01 2009
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