A041459 Denominators of continued fraction convergents to sqrt(245).

1, 1, 2, 3, 23, 141, 1010, 1151, 2161, 3312, 101521, 104833, 206354, 311187, 2384663, 14619165, 104718818, 119337983, 224056801, 343394784, 10525900321, 10869295105, 21395195426, 32264490531, 247246629143, 1515744265389, 10857456486866, 12373200752255

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,103682,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +23*x^14 -141*x^13 +1010*x^12 -1151*x^11 +2161*x^10 -3312*x^9 -2161*x^8 -1151*x^7 -1010*x^6 -141*x^5 -23*x^4 -3*x^3 -2*x^2 -x -1) / ((x^10 -322*x^5 +1)*(x^10 +322*x^5 +1)). - Colin Barker, Nov 18 2013

a(n) = 103682*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[245], 30]] (* Vincenzo Librandi, Dec 18 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 23, 141, 1010, 1151, 2161, 3312, 101521, 104833, 206354, 311187, 2384663, 14619165, 104718818, 119337983, 224056801, 343394784]; [n le 20 select I[n] else 103682*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041458, A040229.

Sequence in context: A370279 A009180 A359840 * A126702 A260126 A260125

Adjacent sequences: A041456 A041457 A041458 * A041460 A041461 A041462

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved