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A042248 Numerators of continued fraction convergents to sqrt(650). 2
25, 51, 2575, 5201, 262625, 530451, 26785175, 54100801, 2731825225, 5517751251, 278619387775, 562756526801, 28416445727825, 57395647982451, 2898198844850375, 5853793337683201, 295587865729010425, 597029524795704051 (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 (0,102,0,-1).

FORMULA

G.f.: (1 + x)*(25 + 26*x - x^2)/((1 - 10*x - x^2)*(1 + 10*x - x^2)) = (25 + 51*x + 25*x^2 - x^3)/(1 - 102*x^2 + x^4). - Vincenzo Librandi, Nov 20 2013

a(n) = 102*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 20 2013

MATHEMATICA

Numerator[Convergents[Sqrt[650], 30]] (* or *) CoefficientList[Series[(25 + 51 x + 25 x^2 - x^3)/(1 - 102 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)

PROG

(MAGMA) I:=[25, 51, 2575, 5201]; [n le 4 select I[n] else 102*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 20 2013

CROSSREFS

Cf. A042249.

Sequence in context: A042242 A042244 A042246 * A132766 A039412 A199990

Adjacent sequences:  A042245 A042246 A042247 * A042249 A042250 A042251

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 8 05:55 EDT 2020. Contains 333312 sequences. (Running on oeis4.)