OFFSET
0,1
COMMENTS
lim_{n -> infinity} a(n+1)/a(n) = 3+2*sqrt(2).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-7,1).
FORMULA
a(n) = 6*a(n-1) - a(n-2) + 34 for n > 1; a(0) = 28, a(1) = 207.
a(n) = ((73+53*sqrt(2))*(3+2*sqrt(2))^n + (73-53*sqrt(2))*(3-2*sqrt(2))^n - 34)/4.
G.f.: (28+11*x-5*x^2)/((1-x)*(1-6*x+x^2)).
MATHEMATICA
Table[(10*LucasL[2*n+3, 2] + 3*LucasL[2*n+1, 2] -34)/4, {n, 0, 50}] (* or *) LinearRecurrence[{7, -7, 1}, {28, 207, 1248}, 50] (* G. C. Greubel, Aug 21 2018 *)
PROG
(PARI) {m=19; v=concat([28, 207, 1248], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}
(Magma) I:=[28, 207, 1248]; [n le 3 select I[n] else 7*Self(n-1) - 7*Self(n-2) + Self(n-3): n in [1..50]]; // G. C. Greubel, Aug 21 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jan 30 2009
EXTENSIONS
Comment and recursion formula added, cross-references edited by Klaus Brockhaus, Sep 23 2009
STATUS
approved