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A042196 Numerators of continued fraction convergents to sqrt(623). 2
24, 25, 599, 624, 30551, 31175, 747576, 778751, 38127624, 38906375, 932974249, 971880624, 47583244201, 48555124825, 1164351115176, 1212906240001, 59383850635224, 60596756875225, 1453109258765399 (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 (0,0,0,1248,0,0,0,-1).

FORMULA

G.f.: (24 +25*x +599*x^2 +624*x^3 +599*x^4 -25*x^5 +24*x^6 -x^7)/(1 -1248*x^4 +x^8). - Vincenzo Librandi, Nov 18 2013

a(n) = 1248*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 18 2013

MATHEMATICA

Numerator[Convergents[Sqrt[623], 30]] (* or *) CoefficientList[Series[(24 + 25 x + 599 x^2 + 624 x^3 + 599 x^4 - 25 x^5 + 24 x^6 - x^7)/(1 - 1248 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 18 2013 *)

PROG

(MAGMA) I:=[24, 25, 599, 624, 30551, 31175, 747576, 778751]; [n le 8 select I[n] else 1248*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

CROSSREFS

Cf. A042197.

Sequence in context: A042190 A042192 A042194 * A042197 A042198 A002924

Adjacent sequences:  A042193 A042194 A042195 * A042197 A042198 A042199

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)