A041559 Denominators of continued fraction convergents to sqrt(297).

1, 4, 13, 17, 30, 77, 107, 184, 659, 2820, 96539, 388976, 1263467, 1652443, 2915910, 7484263, 10400173, 17884436, 64053481, 274098360, 9383397721, 37807689244, 122806465453, 160614154697, 283420620150, 727455394997, 1010876015147, 1738331410144

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,97198,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -4*x^17 +13*x^16 -17*x^15 +30*x^14 -77*x^13 +107*x^12 -184*x^11 +659*x^10 -2820*x^9 -659*x^8 -184*x^7 -107*x^6 -77*x^5 -30*x^4 -17*x^3 -13*x^2 -4*x -1) / (x^20 -97198*x^10 +1). - Colin Barker, Nov 19 2013

a(n) = 97198*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[297], 30]] (* Vincenzo Librandi, Dec 20 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 97198, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 4, 13, 17, 30, 77, 107, 184, 659, 2820, 96539, 388976, 1263467, 1652443, 2915910, 7484263, 10400173, 17884436, 64053481, 274098360}, 30] (* Harvey P. Dale, Sep 26 2023 *)

Prog

(Magma) I:=[1, 4, 13, 17, 30, 77, 107, 184, 659, 2820, 96539, 388976, 1263467, 1652443, 2915910, 7484263, 10400173, 17884436, 64053481, 274098360]; [n le 20 select I[n] else 97198*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041558, A040279.

Sequence in context: A107462 A190863 A022132 * A339272 A280385 A190122

Adjacent sequences: A041556 A041557 A041558 * A041560 A041561 A041562

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved