OFFSET
0,1
LINKS
FORMULA
a(n)=b1^n+b2^n+b3^n where b1, b2, b3 are the roots of x^3-2*x^2-3*x+2.
Limit a[n]/a[n-1] as n -> infinity is the largest root.
MATHEMATICA
b3 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[3]] b2 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[2]] b1 = x /. NSolve[x^3 - 2*x^2 - 3*x + 2 == 0, x][[1]] digits = 25 a = Table[2*(b3^n + b1^n + b2^n)/(b3 + b2 + b1), {n, 0, digits}]
PROG
(PARI) a(n)=if(n<0, 0, polsym(x^3-2*x^2-3*x+2, n)[n+1])
(PARI) a(n)=([0, 1, 0; 0, 0, 1; -2, 3, 2]^n*[3; 2; 10])[1, 1] \\ Charles R Greathouse IV, Jul 21 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, May 22 2005
EXTENSIONS
Edited by N. J. A. Sloane, Jun 08 2007
STATUS
approved