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A182615
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Greatest k such that floor(k/r^n)=n, where r = golden mean = (1+sqrt(5))/2.
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1
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3, 7, 16, 34, 66, 125, 232, 422, 760, 1352, 2388, 4185, 7294, 12644, 21824, 37518, 64278, 109781, 186980, 317666, 538472, 910868, 1537896, 2592049, 4361786, 7328960, 12297712, 20608762, 34495530, 57675437, 96331168, 160737950, 267960664, 446321504, 742796604, 1235255433
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..36.
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FORMULA
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For n>=3, a(n)=-1+A182614(n)+A000032(n), where A000032 is the sequence of Lucas numbers.
Conjectures from Chai Wah Wu, Jan 12 2023: (Start)
a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) - 2*a(n-4) + 2*a(n-5) + a(n-6) for n > 8.
G.f.: x*(-x^7 - x^6 + 3*x^5 + 4*x^2 - x - 3)/((x - 1)*(x + 1)*(x^2 + x - 1)^2). (End)
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EXAMPLE
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The integers k satisfying floor(k/r^3)=3 are 13,14,15,16, so that a(3)=16.
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PROG
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(PARI) a(n) = floor(((1+sqrt(5))/2)^n*(n+1)) \\ David A. Corneth, May 07 2022
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CROSSREFS
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Cf. A001622, A182614, A000032.
Sequence in context: A002936 A014668 A354909 * A181893 A054455 A178455
Adjacent sequences: A182612 A182613 A182614 * A182616 A182617 A182618
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Nov 22 2010
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EXTENSIONS
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a(23) corrected by Andrey Zabolotskiy, May 07 2022
More terms from David A. Corneth, May 07 2022
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STATUS
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approved
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