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A022391
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Fibonacci sequence beginning 1 21.
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0
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1, 21, 22, 43, 65, 108, 173, 281, 454, 735, 1189, 1924, 3113, 5037, 8150, 13187, 21337, 34524, 55861, 90385, 146246, 236631, 382877, 619508, 1002385, 1621893, 2624278, 4246171, 6870449, 11116620
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OFFSET
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0,2
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COMMENTS
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a(n-1)=sum(P(21;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=20. These are the SW-NE diagonals in P(21;n,k), the (21,1) Pascal triangle. Cf. A093645 for the (10,1) Pascal triangle. Observation by Paul Barry, Apr 29 2004. Proof via recursion relations and comparison of inputs.
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LINKS
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Table of n, a(n) for n=0..29.
Tanya Khovanova, Recursive Sequences
S. Kak, The Golden Mean and the Physics of Aesthetics
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FORMULA
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a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=21. a(-1):=20.
G.f.: (1+20*x)/(1-x-x^2).
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MATHEMATICA
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a={}; b=1; c=21; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 4!}]; a [From Vladimir Joseph Stephan Orlovsky, Sep 18 2008]
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CROSSREFS
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Sequence in context: A141439 A125737 A160782 * A041890 A041892 A041894
Adjacent sequences: A022388 A022389 A022390 * A022392 A022393 A022394
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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