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 A153885 a(n) = ((8 + sqrt(5))^n - (8 - sqrt(5))^n)/(2*sqrt(5)). 1
 1, 16, 197, 2208, 23705, 249008, 2585533, 26677056, 274286449, 2814636880, 28851289589, 295557057504, 3026686834313, 30989122956272, 317251444075885, 3247664850794112, 33244802412228577, 340304612398804624, 3483430456059387941, 35656915165420734240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sixth binomial transform of A048879. lim_{n -> infinity} a(n)/a(n-1) = 8 + sqrt(5) = 10.236067977499789696.... LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (16, -59). FORMULA From Philippe Deléham, Jan 03 2009: (Start) a(n) = 16*a(n-1) - 59*a(n-2) for n>1, with a(0)=0, a(1)=1. G.f.: x/(1 - 16*x + 59*x^2). (End) MATHEMATICA Join[{a=1, b=16}, Table[c=16*b-59*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011*) LinearRecurrence[{16, -59}, {1, 16}, 25] (* or *) Table[((8 + sqrt(5))^n - (8 - sqrt(5))^n)/(2*sqrt(5)) , {n, 1, 25}] (* G. C. Greubel, Aug 31 2016 *) PROG (Magma) Z:= PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((8+r)^n-(8-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; # Klaus Brockhaus, Jan 04 2009 (Magma) I:=[1, 16]; [n le 2 select I[n] else 16*Self(n-1)-59*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 01 2016 CROSSREFS Cf. A002163 (decimal expansion of sqrt(5)), A048879. Sequence in context: A103721 A144844 A093060 * A016226 A332854 A154240 Adjacent sequences: A153882 A153883 A153884 * A153886 A153887 A153888 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jan 03 2009 EXTENSIONS Extended beyond a(7) by Klaus Brockhaus, Jan 04 2009 Edited by Klaus Brockhaus, Oct 11 2009 STATUS approved

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Last modified December 2 17:51 EST 2022. Contains 358510 sequences. (Running on oeis4.)