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A041852 Numerators of continued fraction convergents to sqrt(448). 2
21, 127, 5355, 32257, 1360149, 8193151, 345472491, 2081028097, 87748652565, 528572943487, 22287812279019, 134255446617601, 5661016570218261, 34100354867927167, 1437875921023159275 (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 (0,254,0,-1).

FORMULA

G.f.: (21 + 127*x + 21*x^2 - x^3)/(1 - 254*x^2 + x^4). - Vincenzo Librandi, Nov 10 2013

a(n) = 254*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 10 2013

MATHEMATICA

Numerator[Convergents[Sqrt[448], 30]] (* or *) CoefficientList[Series[(21 + 127 x + 21 x^2 - x^3)/(1 - 254 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 10 2013 *)

PROG

(Magma) I:=[21, 127, 5355, 32257]; [n le 4 select I[n] else 254*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 10 2013

CROSSREFS

Cf. A041853.

Sequence in context: A316310 A317265 A213565 * A220712 A295916 A124117

Adjacent sequences: A041849 A041850 A041851 * A041853 A041854 A041855

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 26 18:12 EST 2022. Contains 358362 sequences. (Running on oeis4.)