A041129 Denominators of continued fraction convergents to sqrt(73).

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

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: A106804 A361219 A213098 * A332524 A037490 A037570

Adjacent sequences: A041126 A041127 A041128 * A041130 A041131 A041132

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved