A042049 Denominators of continued fraction convergents to sqrt(548).

1, 2, 5, 17, 22, 127, 149, 1617, 1766, 10447, 12213, 47086, 106385, 259856, 12059761, 24379378, 60818517, 206834929, 267653446, 1545102159, 1812755605, 19672658209, 21485413814, 127099727279, 148585141093, 572855150558, 1294295442209, 3161446034976

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12166146, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^26 -2*x^25 +5*x^24 -17*x^23 +22*x^22 -127*x^21 +149*x^20 -1617*x^19 +1766*x^18 -10447*x^17 +12213*x^16 -47086*x^15 +106385*x^14 -259856*x^13 -106385*x^12 -47086*x^11 -12213*x^10 -10447*x^9 -1766*x^8 -1617*x^7 -149*x^6 -127*x^5 -22*x^4 -17*x^3 -5*x^2 -2*x -1)/(x^28 -12166146*x^14 +1). - Vincenzo Librandi, Jan 13 2014

a(n) = 12166146*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Jan 13 2014

Mathematica

Denominator[Convergents[Sqrt[548], 30]] (* or *) CoefficientList[Series[-(x^26 - 2 x^25 + 5 x^24 - 17 x^23 + 22 x^22 - 127 x^21 + 149 x^20 - 1617 x^19 + 1766 x^18 - 10447 x^17 + 12213 x^16 - 47086 x^15 + 106385 x^14 - 259856 x^13 - 106385 x^12 - 47086 x^11 - 12213 x^10 - 10447 x^9 - 1766 x^8 - 1617 x^7 - 149 x^6 - 127 x^5 - 22 x^4 - 17 x^3 - 5 x^2 - 2 x - 1)/(x^28 - 12166146 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 13 2014 *)

Prog

(Magma) I:=[1, 2, 5, 17, 22, 127, 149, 1617, 1766, 10447, 12213, 47086, 106385, 259856, 12059761, 24379378, 60818517, 206834929, 267653446, 1545102159, 1812755605, 19672658209, 21485413814, 127099727279, 148585141093, 572855150558, 1294295442209, 3161446034976]; [n le 28 select I[n] else 12166146*Self(n-14)-Self(n-28): n in [1..30]]; // Vincenzo Librandi, Jan 13 2014

Crossrefs

Cf. A042048.

Sequence in context: A156010 A215273 A041283 * A341017 A069689 A307479

Adjacent sequences: A042046 A042047 A042048 * A042050 A042051 A042052

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Jan 13 2014

Status

approved