A042493 Denominators of continued fraction convergents to sqrt(774).

1, 1, 5, 6, 11, 28, 39, 67, 307, 374, 20503, 20877, 104011, 124888, 228899, 582686, 811585, 1394271, 6388669, 7782940, 426667429, 434450369, 2164468905, 2598919274, 4763388179, 12125695632, 16889083811, 29014779443, 132948201583, 161962981026, 8878949176987

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, 20810, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +5*x^16 -6*x^15 +11*x^14 -28*x^13 +39*x^12 -67*x^11 +307*x^10 -374*x^9 -307*x^8 -67*x^7 -39*x^6 -28*x^5 -11*x^4 -6*x^3 -5*x^2 -x -1) / (x^20 -20810*x^10 +1). - Colin Barker, Dec 15 2013

a(n) = 20810*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[774], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 20810, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 5, 6, 11, 28, 39, 67, 307, 374, 20503, 20877, 104011, 124888, 228899, 582686, 811585, 1394271, 6388669, 7782940, 426667429}, 40] (* Harvey P. Dale, Jun 29 2015 *)

Prog

(Magma) I:=[1, 1, 5, 6, 11, 28, 39, 67, 307, 374, 20503, 20877, 104011, 124888, 228899, 582686, 811585, 1394271, 6388669, 7782940]; [n le 20 select I[n] else 20810*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A042492, A040746.

Sequence in context: A046828 A328095 A046830 * A042217 A041355 A041050

Adjacent sequences: A042490 A042491 A042492 * A042494 A042495 A042496

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 15 2013

Status

approved