OFFSET
1,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 8 + sqrt(3) = 9.73205080756887729....
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (16, -61).
FORMULA
G.f.: x/(1 - 16*x + 61*x^2). - Klaus Brockhaus, Dec 31 2008, (corrected Oct 11 2009)
a(n) = 16*a(n-1) - 61*a(n-2) for n>1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009
MATHEMATICA
Join[{a=1, b=16}, Table[c=16*b-61*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)
Simplify/@Table[c=Sqrt[3]; ((8+c)^n-(8-c)^n)/(2c), {n, 20}] (* or *) LinearRecurrence[{16, -61}, {1, 16}, 20] (* Harvey P. Dale, Sep 24 2012 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((8+r)^n-(8-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008
(Magma) I:=[1, 16]; [n le 2 select I[n] else 16*Self(n-1)-61*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 23 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Dec 31 2008
Edited by Klaus Brockhaus, Oct 11 2009
STATUS
approved