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A153885
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a(n) = ((8+sqrt(5))^n-(8-sqrt(5))^n)/(2*sqrt(5)).
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0
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1, 16, 197, 2208, 23705, 249008, 2585533, 26677056, 274286449, 2814636880, 28851289589, 295557057504, 3026686834313, 30989122956272, 317251444075885, 3247664850794112, 33244802412228577, 340304612398804624
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OFFSET
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1,2
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COMMENTS
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Sixth binomial transform of A048879.
lim_{n -> infinity} a(n)/a(n-1) = 8+sqrt(5) = 10.236067977499789696....
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LINKS
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Table of n, a(n) for n=1..18.
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FORMULA
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a(n) = 16*a(n-1)-59*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-16*x+59*x^2). [From Philippe DELEHAM, Jan 03 2009]
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MATHEMATICA
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Join[{a=1, b=16}, Table[c=16*b-59*a; a=b; b=c, {n, 40}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)
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PROG
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((8+r)^n-(8-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Jan 04 2009]
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CROSSREFS
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Cf. A002163 (decimal expansion of sqrt(5)), A048879.
Sequence in context: A103721 A144844 A093060 * A016226 A154240 A081679
Adjacent sequences: A153882 A153883 A153884 * A153886 A153887 A153888
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jan 03 2009
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus, Jan 04 2009
Edited by Klaus Brockhaus, Oct 11 2009
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STATUS
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approved
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