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A042284 Numerators of continued fraction convergents to sqrt(668). 2
25, 26, 155, 336, 4187, 8710, 47737, 56447, 2870087, 2926534, 17502757, 37932048, 472687333, 983306714, 5389220903, 6372527617, 324015601753, 330388129370, 1975956248603, 4282300626576, 53363563767515 (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 (0,0,0,0,0,0,0,112894,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: (25 +26*x +155*x^2 +336*x^3 +4187*x^4 +8710*x^5 +47737*x^6 +56447*x^7 +47737*x^8 -8710*x^9 +4187*x^10 -336*x^11 +155*x^12 -26*x^13 +25*x^14 -x^15)/((1 -336*x^4 +x^8)*(1 +336*x^4 +x^8)). - Vincenzo Librandi, Nov 20 2013

a(n) = 112894*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 18 2013

MATHEMATICA

Numerator[Convergents[Sqrt[668], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 155 x^2 + 336 x^3 + 4187 x^4 + 8710 x^5 + 47737 x^6 + 56447 x^7 + 47737 x^8 - 8710 x^9 + 4187 x^10 - 336 x^11 + 155 x^12 - 26 x^13 + 25 x^14 - x^15)/(1 - 112894 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)

PROG

(MAGMA) I:=[25, 26, 155, 336, 4187, 8710, 47737, 56447, 2870087, 2926534, 17502757, 37932048, 472687333, 983306714, 5389220903, 6372527617]; [n le 16 select I[n] else 112894*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

CROSSREFS

Cf. A042285.

Sequence in context: A042276 A042282 A042280 * A042286 A042288 A042290

Adjacent sequences:  A042281 A042282 A042283 * A042285 A042286 A042287

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 14 05:10 EDT 2021. Contains 345018 sequences. (Running on oeis4.)