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A042296 Numerators of continued fraction convergents to sqrt(674). 2
25, 26, 649, 675, 34399, 35074, 876175, 911249, 46438625, 47349874, 1182835601, 1230185475, 62692109351, 63922294826, 1596827185175, 1660749480001, 84634301185225, 86295050665226, 2155715517150649 (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 (0,0,0,1350,0,0,0,-1).

FORMULA

G.f.: (25 +26*x +649*x^2 +675*x^3 +649*x^4 -26*x^5 +25*x^6 -x^7)/(1 -1350*x^4 +x^8). - Vincenzo Librandi, Nov 21 2013

a(n) = 1350*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 21 2013

MATHEMATICA

Numerator[Convergents[Sqrt[674], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 649 x^2 + 675 x^3 + 649 x^4 - 26 x^5 + 25 x^6 - x^7)/(1 - 1350 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

LinearRecurrence[{0, 0, 0, 1350, 0, 0, 0, -1}, {25, 26, 649, 675, 34399, 35074, 876175, 911249}, 20] (* Harvey P. Dale, Jul 01 2017 *)

PROG

(MAGMA) I:=[25, 26, 649, 675, 34399, 35074, 876175, 911249]; [n le 8 select I[n] else 1350*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

CROSSREFS

Cf. A042297.

Sequence in context: A042292 A042294 A041311 * A042297 A042298 A157091

Adjacent sequences:  A042293 A042294 A042295 * A042297 A042298 A042299

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 21 10:45 EDT 2021. Contains 343150 sequences. (Running on oeis4.)