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A041129 Denominators of continued fraction convergents to sqrt(73). 2
1, 1, 2, 11, 57, 68, 125, 2068, 2193, 4261, 23498, 121751, 145249, 267000, 4417249, 4684249, 9101498, 50191739, 260060193, 310251932, 570312125, 9435245932, 10005558057, 19440803989, 107209578002, 555488693999, 662698272001, 1218186966000, 20153689728001 (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 (0,0,0,0,0,0,2136,0,0,0,0,0,0,1).

FORMULA

G.f.: -(x^12 -x^11 +2*x^10 -11*x^9 +57*x^8 -68*x^7 +125*x^6 +68*x^5 +57*x^4 +11*x^3 +2*x^2 +x +1) / (x^14 +2136*x^7 -1). - Colin Barker, Nov 13 2013

a(n) = 2136*a(n-7) + a(n-14). - Vincenzo Librandi, Dec 11 2013

MATHEMATICA

Denominator/@Convergents[Sqrt[73], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)

CoefficientList[Series[-(x^12 - x^11 + 2 x^10 - 11 x^9 + 57 x^8 - 68 x^7 + 125 x^6 + 68 x^5 + 57 x^4 + 11 x^3 + 2 x^2 + x + 1)/(x^14 + 2136 x^7 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

PROG

(MAGMA) I:=[1, 1, 2, 11, 57, 68, 125, 2068, 2193, 4261, 23498, 121751, 145249, 267000]; [n le 14 select I[n] else 2136*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

CROSSREFS

Cf. A041128, A010151, A020830, A010525.

Sequence in context: A037554 A106804 A213098 * A332524 A037490 A037570

Adjacent sequences:  A041126 A041127 A041128 * A041130 A041131 A041132

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 8 08:27 EST 2021. Contains 341942 sequences. (Running on oeis4.)