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Search: id:A153885
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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
1
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| 1, 16, 197, 2208, 23705, 249008, 2585533, 26677056, 274286449, 2814636880, 28851289589, 295557057504, 3026686834313, 30989122956272, 317251444075885, 3247664850794112, 33244802412228577, 340304612398804624
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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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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 (kolotoko(AT)wanadoo.fr), Jan 03 2009]
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PROGRAM
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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 (klaus-brockhaus(AT)t-online.de), 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 this_sequence A016226 A154240 A081679
Adjacent sequences: A153882 A153883 A153884 this_sequence 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 (klaus-brockhaus(AT)t-online.de), Jan 04 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 11 2009
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