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A042742 Numerators of continued fraction convergents to sqrt(902). 2
30, 901, 54090, 1623601, 97470150, 2925728101, 175641156210, 5272160414401, 316505266020270, 9500430141022501, 570342313727370330, 17119769841962132401, 1027756532831455314390, 30849815754785621564101, 1852016701819968749160450, 55591350870353848096377601 (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 (0,1802,0,-1).

FORMULA

G.f.: -(x^3-30*x^2-901*x-30) / (x^4-1802*x^2+1). - Vincenzo Librandi, Dec 03 2013, simplified by Colin Barker, Dec 27 2013

a(n) = 1802*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013, simplified by Colin Barker, Dec 27 2013

MATHEMATICA

Numerator[Convergents[Sqrt[902], 30]] (* or *) CoefficientList[Series[(30 + 901 x + 30 x^2 - x^3)/(1 - 1802 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)

PROG

(MAGMA) I:=[30, 901, 54090, 1623601]; [n le 4 select I[n] else 1802*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

CROSSREFS

Cf. A042743, A040871.

Sequence in context: A171304 A009974 A041421 * A144350 A111216 A158672

Adjacent sequences:  A042739 A042740 A042741 * A042743 A042744 A042745

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 03 2013

STATUS

approved

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Last modified May 7 19:47 EDT 2021. Contains 343652 sequences. (Running on oeis4.)