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1, 2, 8, 21, 60, 160, 429, 1134, 2992, 7865, 20648, 54144, 141897, 371722, 973560, 2549421, 6675460, 17478176, 45761045, 119808150, 313668576, 821205937, 2149962768, 5628704256, 14736185425, 38579909330, 101003635304
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OFFSET
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1,2
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COMMENTS
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a(n)/a(n-1) tends to phi^2.
A143212(n) = Product of sum of first n Fibonacci numbers and Fibonacci number(n). - Vladimir Joseph Stephan Orlovsky, Oct 13 2009
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LINKS
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Table of n, a(n) for n=1..27.
Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1).
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FORMULA
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a(n) = F(n) * (F(n+2)-1) = A000045(n) * A000071(n+2) = row sums of triangle A143211.
From R. J. Mathar, Sep 06 2008: (Start)
G.f.: (1-x+x^2)/((1+x)(1-3x+x^2)(1-x-x^2)).
a(n) = -A000045(n+1) + 3*(-1)^n/5 + 7*A001906(n+1)/5 -3*A001906(n)/5. (End)
a(n) = F(n)*sum{k=0..n} F(k). - Paul Barry, Jan 05 2009
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EXAMPLE
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a(5) = 60 = F(5) * (F(7)-1) = 5*12.
a(5) = 60 = sum of row 5 terms of triangle A143211: (5 + 5 + 10 + 15 + 25).
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MATHEMATICA
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Clear[lst, n, a, f]; a=0; lst={}; Do[f=Fibonacci[n]; a+=f; AppendTo[lst, a*Fibonacci[n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 13 2009 *)
Table[Fibonacci[n](Fibonacci[n+2]-1), {n, 30}] (* Harvey P. Dale, Dec 14 2012 *)
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CROSSREFS
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Cf. A000045, A000071, A143211.
Sequence in context: A123044 A143229 A123285 * A316270 A219970 A107361
Adjacent sequences: A143209 A143210 A143211 * A143213 A143214 A143215
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson, Jul 30 2008
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STATUS
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approved
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