OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,50,0,-1).
FORMULA
G.f.: (12+25*x+12*x^2-x^3)/(1-50*x^2+x^4). - Vincenzo Librandi, Nov 01 2013
a(n) = 50*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 01 2013
a(n) = (12 + sqrt(13) + (12 - sqrt(13))*(-1)^n)*cosh(n*arccosh(25)/2)/2 + sqrt(3)*(1 + sqrt(13) + (sqrt(13) - 1)*(-1)^n)*sinh(n*arccosh(25)/2). - Stefano Spezia, Jul 05 2022
MATHEMATICA
Numerator[Convergents[Sqrt[156], 30]] (* or *) CoefficientList[Series[(12 + 25 x + 12 x^2 - x^3)/(1 - 50 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 01 2013 *)
PROG
(Magma) I:=[12, 25, 612, 1249]; [n le 4 select I[n] else 50*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 01 2013
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved