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A042416 Numerators of continued fraction convergents to sqrt(736). 2
27, 190, 217, 624, 841, 2306, 3147, 24335, 1317237, 9244994, 10562231, 30369456, 40931687, 112232830, 153164517, 1184384449, 64109924763, 449953857790, 514063782553, 1478081422896, 1992145205449 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,48670,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^15 -27*x^14 +190*x^13 -217*x^12 +624*x^11 -841*x^10 +2306*x^9 -3147*x^8 -24335*x^7 -3147*x^6 -2306*x^5 -841*x^4 -624*x^3 -217*x^2 -190*x -27)/(x^16 -48670*x^8 +1). - Vincenzo Librandi, Nov 23 2013

a(n) = 48670*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 23 2013

MATHEMATICA

Numerator[Convergents[Sqrt[736], 30]] (* or *) CoefficientList[Series[-(x^15 - 27 x^14 + 190 x^13 - 217 x^12 + 624 x^11 - 841 x^10 + 2306 x^9 - 3147 x^8 - 24335 x^7 - 3147 x^6 - 2306 x^5 - 841 x^4 - 624 x^3 - 217 x^2 - 190 x - 27)/(x^16 - 48670 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)

PROG

(MAGMA) I:=[27, 190, 217, 624, 841, 2306, 3147, 24335, 1317237, 9244994, 10562231, 30369456, 40931687, 112232830, 153164517, 1184384449]; [n le 16 select I[n] else 48670*Self(n-8)-Self(n-16): n in [1..30]]; //  Vincenzo Librandi, Nov 23 2013

CROSSREFS

Cf. A042417.

Sequence in context: A258637 A228463 A000499 * A216108 A216110 A216112

Adjacent sequences:  A042413 A042414 A042415 * A042417 A042418 A042419

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)