A042024 Numerators of continued fraction convergents to sqrt(536).

23, 139, 162, 301, 764, 4121, 9006, 13127, 22133, 145925, 6734683, 40554023, 47288706, 87842729, 222974164, 1202713549, 2628401262, 3831114811, 6459516073, 42588211249, 1965517233527, 11835691612411

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,291850,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: (23 +139*x +162*x^2 +301*x^3 +764*x^4 +4121*x^5 +9006*x^6 +13127*x^7 +22133*x^8 +145925*x^9 +22133*x^10 -13127*x^11 +9006*x^12 -4121*x^13 +764*x^14 -301*x^15 +162*x^16 -139*x^17 +23*x^18 -x^19) / (1 -291850*x^10 +x^20). - Vincenzo Librandi, Nov 13 2013

a(n) = 291850*a(n-10)-a(n-20): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013

Mathematica

Numerator[Convergents[Sqrt[536], 30]] (* or *) CoefficientList[Series[(23 + 139 x + 162 x^2 + 301 x^3 + 764 x^4 + 4121 x^5 + 9006 x^6 + 13127 x^7 + 22133 x^8 + 145925 x^9 + 22133 x^10 - 13127 x^11 + 9006 x^12 - 4121 x^13 + 764 x^14 - 301 x^15 + 162 x^16 - 139 x^17 + 23 x^18 - x^19)/(1 - 291850 x^10 + x^20), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 14 2013 *)

Prog

(Magma) I:=[23, 139, 162, 301, 764, 4121, 9006, 13127, 22133, 145925, 6734683, 40554023, 47288706, 87842729, 222974164, 1202713549, 2628401262, 3831114811, 6459516073, 42588211249]; [n le 20 select I[n] else 291850*Self(n-10)-Self(n-20): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013

Crossrefs

Cf. A042025.

Sequence in context: A254758 A057883 A160221 * A141999 A059915 A059701

Adjacent sequences: A042021 A042022 A042023 * A042025 A042026 A042027

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved