OFFSET
0,3
COMMENTS
Interspersion of 4 linear recurrences with constant coefficients. - Gerry Martens, Jun 10 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,62,0,0,0,-1).
FORMULA
G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / ((x^4-8*x^2+1)*(x^4+8*x^2+1)). - Colin Barker, Nov 12 2013
a(n) = 62*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013
MAPLE
numtheory:-cfrac(sqrt(60), 100, 'con', 'den'):
den[1..-2]; # Robert Israel, Jun 09 2015
MATHEMATICA
Denominator[Convergents[Sqrt[60], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
d0 := LinearRecurrence[{62, -1}, {1, 59}, 20]
d1 := LinearRecurrence[{62, -1}, {1, 63}, 20] (* A258684 *)
d2 := LinearRecurrence[{62, -1}, {3, 185}, 20]
d3 := LinearRecurrence[{62, -1}, {4, 248}, 20]
Flatten[MapIndexed[{d0[[#]] , d1[[#]], d2[[#]] , d3[[#]]} &,
Range[10]]] (* Gerry Martens, Jun 09 2015 *)
LinearRecurrence[{0, 0, 0, 62, 0, 0, 0, -1}, {1, 1, 3, 4, 59, 63, 185, 248}, 30] (* Ray Chandler, Aug 03 2015 *)
PROG
(Magma) I:=[1, 1, 3, 4, 59, 63, 185, 248]; [n le 8 select I[n] else 62*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
KEYWORD
nonn,cofr,easy,frac
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 12 2013
STATUS
approved