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A041191

Denominators of continued fraction convergents to sqrt(106).

1, 3, 7, 10, 17, 27, 44, 115, 389, 7895, 24074, 56043, 80117, 136160, 216277, 352437, 921151, 3115890, 63238951, 192832743, 448904437, 641737180, 1090641617, 1732378797, 2823020414, 7378419625, 24958279289, 506544005405, 1544590295504, 3595724596413

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OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,8010,0,0,0,0,0,0,0,0,1).

FORMULA

G.f.: -(x^16 -3*x^15 +7*x^14 -10*x^13 +17*x^12 -27*x^11 +44*x^10 -115*x^9 +389*x^8 +115*x^7 +44*x^6 +27*x^5 +17*x^4 +10*x^3 +7*x^2 +3*x +1) / (x^18 +8010*x^9 -1). - Colin Barker, Nov 14 2013

a(n) = 8010*a(n-9) + a(n-18). - Vincenzo Librandi, Dec 12 2013

MATHEMATICA

Denominator[Convergents[Sqrt[106], 30]] (* Vincenzo Librandi, Dec 12 2013 *)

PROG

(Magma) I:=[1, 3, 7, 10, 17, 27, 44, 115, 389, 7895, 24074, 56043, 80117, 136160, 216277, 352437, 921151, 3115890]; [n le 18 select I[n] else 8010*Self(n-9)+Self(n-18): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

(Python)

from sympy import sqrt

from sympy.ntheory.continued_fraction import *

def aupton(terms):

g = continued_fraction_convergents(continued_fraction_iterator(sqrt(106)))

return [next(g).denominator for n in range(terms)]

print(aupton(30)) # Michael S. Branicky, Oct 31 2021

CROSSREFS

Cf. A041190, A010172.

Sequence in context: A258864 A111244 A022120 * A304216 A305247 A316547

Adjacent sequences: A041188 A041189 A041190 * A041192 A041193 A041194

KEYWORD