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+(867-578*sqrt(2))*(17+12*sqrt(2))^n+(867+578*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: x*(289-2890*x+289*x^2)/((1-x)*(1-34*x+x^2)). [corrected by Klaus Brockhaus, Sep 23 2009]
a(1)=289, a(2)=7225, a(3)=243049, a(n) = 35*a(n-1)-35*a(n-2)+a(n-3). - Harvey P. Dale, Dec 11 2013
EXAMPLE
a(3) = 34*a(2)-a(1)-2312 = 34*7225-289-2312 = 243049.
MATHEMATICA
RecurrenceTable[{a[1]==289, a[2]==7225, a[n]==34a[n-1]-a[n-2]-2312}, a, {n, 20}] (* or *) LinearRecurrence[{35, -35, 1}, {289, 7225, 243049}, 20] (* Harvey P. Dale, Dec 11 2013 *)
PROG
(PARI) {m=14; v=concat([289, 7225], 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
STATUS
approved