OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,36,0,0,0,0,1).
FORMULA
From Johannes W. Meijer, Jun 12 2010: (Start)
a(5*n) = A006190(3*n+1),
G.f.: ((1 - 2*x + 4*x^2 - 3*x^3 + x^4)*(1 + 3*x + 4*x^2 + 2*x^3 + x^4))/(1 - 36*x^5 - x^10). - Peter J. C. Moses, Jul 29 2013
a(n) = A010122(n)*a(n-1) + a(n-2), a(0)=1, a(-1)=0. - Paul Weisenhorn, Aug 17 2018
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[13], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011 *)
CoefficientList[Series[((1 - 2 x + 4 x^2 - 3 x^3 + x^4) (1 + 3 x + 4 x^2 + 2 x^3 + x^4))/(1 - 36 x^5 - x^10), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2013 *)
LinearRecurrence[{0, 0, 0, 0, 36, 0, 0, 0, 0, 1}, {1, 1, 2, 3, 5, 33, 38, 71, 109, 180}, 40] (* Harvey P. Dale, Sep 30 2016 *)
PROG
(Magma) I:=[1, 1, 2, 3, 5, 33, 38, 71, 109, 180]; [n le 10 select I[n] else 36*Self(n-5)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 10 2013
STATUS
approved