A041653 Denominators of continued fraction convergents to sqrt(345).

1, 1, 2, 5, 7, 47, 54, 155, 209, 364, 13313, 13677, 26990, 67657, 94647, 635539, 730186, 2095911, 2826097, 4922008, 180018385, 184940393, 364958778, 914857949, 1279816727, 8593758311, 9873575038, 28340908387, 38214483425, 66555391812, 2434208588657

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, 13522, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -5*x^15 +7*x^14 -47*x^13 +54*x^12 -155*x^11 +209*x^10 -364*x^9 -209*x^8 -155*x^7 -54*x^6 -47*x^5 -7*x^4 -5*x^3 -2*x^2 -x -1) / (x^20 -13522*x^10 +1). - Colin Barker, Nov 20 2013

a(n) = 13522*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[345], 30]] (* Vincenzo Librandi, Dec 22 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 13522, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 5, 7, 47, 54, 155, 209, 364, 13313, 13677, 26990, 67657, 94647, 635539, 730186, 2095911, 2826097, 4922008}, 40] (* Harvey P. Dale, Oct 21 2015 *)

Prog

(Magma) I:=[1, 1, 2, 5, 7, 47, 54, 155, 209, 364, 13313, 13677, 26990, 67657, 94647, 635539, 730186, 2095911, 2826097, 4922008]; [n le 20 select I[n] else 13522*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041652, A040326.

Sequence in context: A174259 A215213 A069356 * A182785 A358381 A041125

Adjacent sequences: A041650 A041651 A041652 * A041654 A041655 A041656

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved