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Search: id:A066629
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| A066629 |
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2*Fibonacci(n+2) + [(-1)^n - 3]/2. |
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+0
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; listen)
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OFFSET
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0,2
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COMMENT
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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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FORMULA
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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]
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EXAMPLE
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a(5)=A(5,0)+A(4,1)+A(3,2)=6+11+7=24
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PROGRAM
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(PARI) print1(y=1, ", ", z=2, ", "); for(n=2, 35, print1(a=z+y+2-n%2, ", "); y=z; z=a)
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CROSSREFS
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Cf. A051597.
A153864 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 03 2009]
Sequence in context: A073335 A066897 A078697 this_sequence A154327 A074027 A018156
Adjacent sequences: A066626 A066627 A066628 this_sequence A066630 A066631 A066632
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Dec 18 2002
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EXTENSIONS
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Extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 19 2002
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