A041909 Denominators of continued fraction convergents to sqrt(476).

1, 1, 5, 11, 115, 241, 1079, 1320, 56519, 57839, 287875, 633589, 6623765, 13881119, 62148241, 76029360, 3255381361, 3331410721, 16581024245, 36493459211, 381515616355, 799524691921, 3579614384039, 4379139075960, 187503455574359, 191882594650319

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, 0, 0, 0, 57598, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -x^13 +5*x^12 -11*x^11 +115*x^10 -241*x^9 +1079*x^8 -1320*x^7 -1079*x^6 -241*x^5 -115*x^4 -11*x^3 -5*x^2 -x -1) / ((x^8 -240*x^4 +1)*(x^8 +240*x^4 +1)). - Colin Barker, Nov 27 2013

a(n) = 57598*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 27 2013

Mathematica

Denominator[Convergents[Sqrt[476], 30]] (* Vincenzo Librandi, Dec 27 2013 *)

Prog

(Magma) I:=[1, 1, 5, 11, 115, 241, 1079, 1320, 56519, 57839, 287875, 633589, 6623765, 13881119, 62148241, 76029360]; [n le 16 select I[n] else 57598*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 27 2013

Crossrefs

Cf. A041908, A040454.

Sequence in context: A057178 A056265 A302144 * A041048 A354022 A222568

Adjacent sequences: A041906 A041907 A041908 * A041910 A041911 A041912

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved