A041375 Denominators of continued fraction convergents to sqrt(202).

1, 4, 5, 14, 33, 47, 221, 6235, 25161, 31396, 87953, 207302, 295255, 1388322, 39168271, 158061406, 197229677, 552520760, 1302271197, 1854791957, 8721439025, 246055084657, 992941777653, 1238996862310, 3470935502273, 8180867866856, 11651803369129

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,6282,0,0,0,0,0,0,1).

Formula

G.f.: -(x^12 -4*x^11 +5*x^10 -14*x^9 +33*x^8 -47*x^7 +221*x^6 +47*x^5 +33*x^4 +14*x^3 +5*x^2 +4*x +1) / (x^14 +6282*x^7 -1). - Colin Barker, Nov 16 2013

a(n) = 6282*a(n-7) + a(n-14). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[202], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 4, 5, 14, 33, 47, 221, 6235, 25161, 31396, 87953, 207302, 295255, 1388322]; [n le 14 select I[n] else 6282*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041374, A040187.

Sequence in context: A007084 A216243 A093862 * A042279 A352683 A182252

Adjacent sequences: A041372 A041373 A041374 * A041376 A041377 A041378

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved