OFFSET
1,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 7 + sqrt(6) = 9.4494897427....
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (14, -43).
FORMULA
From Philippe Deléham, Jan 06 2009: (Start)
a(n) = 14*a(n-1) - 43*a(n-2)for n>1, with a(0)=0, a(1)=1.
G.f.: x/(1 - 14x + 43x^2). (End)
E.g.f.: sinh(sqrt(6)*x)*exp(7*x)/sqrt(6). - Ilya Gutkovskiy, Sep 07 2016
MATHEMATICA
Join[{a=1, b=14}, Table[c=14*b-43*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{14, -43}, {1, 14}, 25] (* or *) Table[( (7 + sqrt(6))^n - (7 - sqrt(6))^n )/(2*sqrt(6)), {n, 1, 25}] (* G. C. Greubel, Sep 07 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
I:=[1, 14]; [n le 2 select I[n] else 14*Self(n-1)-43*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Sep 07 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Jan 07 2009
Edited by Klaus Brockhaus, Oct 06 2009
STATUS
approved