A153885 a(n) = ((8 + sqrt(5))^n - (8 - sqrt(5))^n)/(2*sqrt(5)).
1, 16, 197, 2208, 23705, 249008, 2585533, 26677056, 274286449, 2814636880, 28851289589, 295557057504, 3026686834313, 30989122956272, 317251444075885, 3247664850794112, 33244802412228577, 340304612398804624, 3483430456059387941, 35656915165420734240
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (16, -59).
Programs
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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
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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 *)
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)
Extensions
Extended beyond a(7) by Klaus Brockhaus, Jan 04 2009
Edited by Klaus Brockhaus, Oct 11 2009
Comments