OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1000,0,0,0,0,1).
FORMULA
G.f.: -(x^8-2*x^7+7*x^6-23*x^5+53*x^4+23*x^3+7*x^2+2*x+1) / (x^10+1000*x^5-1). - Colin Barker, Nov 14 2013
a(n) = 1000*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 12 2013
MATHEMATICA
Denominator/@Convergents[Sqrt[89], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^8 - 2 x^7 + 7 x^6 - 23 x^5 + 53 x^4 + 23 x^3 + 7 x^2 + 2 x + 1)/(x^10 + 1000 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
LinearRecurrence[{0, 0, 0, 0, 1000, 0, 0, 0, 0, 1}, {1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000}, 30] (* Harvey P. Dale, Feb 07 2019 *)
PROG
(Magma) I:=[1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000]; [n le 10 select I[n] else 1000*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved