OFFSET
1,1
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = (17+12*sqrt(2)).
LINKS
Index entries for linear recurrences with constant coefficients, signature (35,-35,1).
FORMULA
a(n) = (578+(387-182*sqrt(2))*(17+12*sqrt(2))^n+(387+182*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: x*(625-3106*x+169*x^2)/((1-x)*(1-34*x+x^2)).
EXAMPLE
a(3) = 34*a(2)-a(1)-2312 = 34*18769-625-2312 = 635209.
MATHEMATICA
RecurrenceTable[{a[1]==625, a[2]==18769, a[n]==34a[n-1]-a[n-2]-2312}, a, {n, 20}] (* or *) LinearRecurrence[{35, -35, 1}, {625, 18769, 635209}, 20] (* Harvey P. Dale, Sep 29 2016 *)
PROG
(PARI) {m=14; v=concat([625 , 18769], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Feb 09 2009
EXTENSIONS
G.f. corrected by Klaus Brockhaus, Sep 23 2009
STATUS
approved