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A066629
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2*Fibonacci(n+2) + [(-1)^n - 3]/2.
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6
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1, 2, 5, 8, 15, 24, 41, 66, 109, 176, 287, 464, 753, 1218, 1973, 3192, 5167, 8360, 13529, 21890, 35421, 57312, 92735, 150048, 242785, 392834, 635621, 1028456, 1664079, 2692536, 4356617, 7049154, 11405773, 18454928, 29860703, 48315632
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Fibonacci-like numbers made from Asher Auel's triangle A(n,m) (A051597) satisfying A(0,0)=1, A(1,0)=2, A(1,1)=2, etc..: then a(0)=1, a(1)=2, a(n)=A(n,0)+A(n-1,1)+A(n-2,2)+...
a(n)/a(n-1)->(1+sqr5)/2. If n even: a(n)=a(n-1)+a(n-2)+2; if n odd: a(n)=a(n-1)+a(n-2)+1.
Equals row sums of triangle A153864 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 03 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,250
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FORMULA
| G.f.: (1+x+x^2)/((1-x-x^2)(1-x)(1+x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 19 2008]
a(0)=1, a(1)=2, a(2)=5, a(3)=8, a(n)=a(n-1)+2*a(n-2)-a(n-3)-a(n-4) [From Harvey P. Dale, Oct 09 2011]
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EXAMPLE
| a(5)=A(5,0)+A(4,1)+A(3,2)=6+11+7=24
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MATHEMATICA
| Join[{b=1}, a=0; Table[If[OddQ[a]&&EvenQ[b], c=a+b+2, c=a+b+1]; a=b; b=c, {n, 0, 5!}]](*From Vladimir Joseph Stephan Orlovsky, Jan 10 2011*)
Table[2Fibonacci[n+2]+((-1)^n-3)/2, {n, 0, 40}] (* or *) LinearRecurrence[ {1, 2, -1, -1}, {1, 2, 5, 8}, 41] (* From Harvey P. Dale, Oct 09 2011 *)
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PROG
| (PARI) print1(y=1, ", ", z=2, ", "); for(n=2, 35, print1(a=z+y+2-n%2, ", "); y=z; z=a)
(PARI) { for (n=0, 250, a=2*fibonacci(n+2) + ((-1)^n - 3)/2; write("b066629.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Mar 14 2010]
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CROSSREFS
| Cf. A051597.
A153864 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 03 2009]
Sequence in context: A066897 A078697 * A154327 A074027 A018156 A051293
Adjacent sequences: A066626 A066627 A066628 * A066630 A066631 A066632
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KEYWORD
| easy,nonn
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AUTHOR
| Miklos Kristof (kristmikl(AT)freemail.hu), Dec 18 2002
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EXTENSIONS
| Extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 19 2002
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