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A041044 Numerators of continued fraction convergents to sqrt(28). 2
5, 16, 37, 127, 1307, 4048, 9403, 32257, 331973, 1028176, 2388325, 8193151, 84319835, 261152656, 606625147, 2081028097, 21416906117, 66331746448, 154080399013, 528572943487, 5439809833883, 16848002445136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,254,0,0,0,-1).

FORMULA

a(n) = 254*a(n-4)-a(n-8). G.f.: -(x^7-5*x^6+16*x^5-37*x^4-127*x^3-37*x^2-16*x-5)/((x^4-16*x^2+1)*(x^4+16*x^2+1)). [Colin Barker, Jul 16 2012]

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[28], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)

CoefficientList[Series[- (x^7 - 5 x^6 + 16 x^5 - 37 x^4 - 127 x^3 - 37 x^2 - 16 x - 5)/((x^4 - 16 x^2 + 1) (x^4 + 16 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)

CROSSREFS

Cf. A010483, A041045.

Sequence in context: A188427 A022496 A296536 * A042645 A218259 A211807

Adjacent sequences:  A041041 A041042 A041043 * A041045 A041046 A041047

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 5 15:16 EDT 2020. Contains 334850 sequences. (Running on oeis4.)