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<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] ]; # 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
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