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A041653 Denominators of continued fraction convergents to sqrt(345). 2
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 (list; graph; refs; listen; history; text; internal format)
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 A041125 A293592

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

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Last modified June 25 10:29 EDT 2019. Contains 324351 sequences. (Running on oeis4.)