OFFSET
1,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 9 + 2*sqrt(2) = 11.8284271247....
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..900
Index entries for linear recurrences with constant coefficients, signature (18, -73).
FORMULA
G.f.: x/(1 - 18*x + 73*x^2). - Klaus Brockhaus, Jan 12 2009, corrected Oct 08 2009
a(n) = 18*a(n-1) - 73*a(n-2) for n>1, with a(0)=0, a(1)=1. - Philippe Deléham, Jan 12 2009
E.g.f.: (1/(2*sqrt(2)))*exp(9*x)*sinh(2*sqrt(2)*x). - G. C. Greubel, Sep 14 2016
MATHEMATICA
Join[{a=1, b=18}, Table[c=18*b-73*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
LinearRecurrence[{18, -73}, {1, 18}, 25] (* or *) Table[( (9 + 2*sqrt(2))^n - (9 - 2*sqrt(2))^n )/(4*sqrt(2)), {n, 1, 25}] (* G. C. Greubel, Sep 14 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((9+2*r)^n-(9-2*r)^n)/(4*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 12 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Jan 12 2009
Edited by Klaus Brockhaus, Oct 08 2009
STATUS
approved