A041044 Numerators of continued fraction convergents to sqrt(28).

5, 16, 37, 127, 1307, 4048, 9403, 32257, 331973, 1028176, 2388325, 8193151, 84319835, 261152656, 606625147, 2081028097, 21416906117, 66331746448, 154080399013, 528572943487, 5439809833883, 16848002445136

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