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A042264 Numerators of continued fraction convergents to sqrt(658). 2
25, 26, 51, 77, 513, 590, 1103, 1693, 85753, 87446, 173199, 260645, 1737069, 1997714, 3734783, 5732497, 290359633, 296092130, 586451763, 882543893, 5881715121, 6764259014, 12645974135, 19410233149 (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, 3386, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: (25 +26*x +51*x^2 +77*x^3 +513*x^4 +590*x^5 +1103*x^6 +1693*x^7 +1103*x^8 -590*x^9 +513*x^10 -77*x^11 +51*x^12 -26*x^13 +25*x^14 -x^15)/(1 -3386*x^8 +x^16). - Vincenzo Librandi, Nov 20 2013

a(n) = 3386*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 18 2013

MATHEMATICA

Numerator[Convergents[Sqrt[658], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 51 x^2 + 77 x^3 + 513 x^4 + 590 x^5 + 1103 x^6 + 1693 x^7 + 1103 x^8 - 590 x^9 + 513 x^10 - 77 x^11 + 51 x^12 - 26 x^13 + 25 x^14 - x^15)/(1 - 3386 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)

PROG

(MAGMA) I:=[25, 26, 51, 77, 513, 590, 1103, 1693, 85753, 87446, 173199, 260645, 1737069, 1997714, 3734783, 5732497]; [n le 16 select I[n] else 3386*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

CROSSREFS

Cf. A042265.

Sequence in context: A022395 A042260 A042262 * A274063 A042256 A042258

Adjacent sequences:  A042261 A042262 A042263 * A042265 A042266 A042267

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 10 12:15 EDT 2020. Contains 336379 sequences. (Running on oeis4.)