A042196 Numerators of continued fraction convergents to sqrt(623).

24, 25, 599, 624, 30551, 31175, 747576, 778751, 38127624, 38906375, 932974249, 971880624, 47583244201, 48555124825, 1164351115176, 1212906240001, 59383850635224, 60596756875225, 1453109258765399

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1248,0,0,0,-1).

Formula

G.f.: (24 +25*x +599*x^2 +624*x^3 +599*x^4 -25*x^5 +24*x^6 -x^7)/(1 -1248*x^4 +x^8). - Vincenzo Librandi, Nov 18 2013

a(n) = 1248*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[623], 30]] (* or *) CoefficientList[Series[(24 + 25 x + 599 x^2 + 624 x^3 + 599 x^4 - 25 x^5 + 24 x^6 - x^7)/(1 - 1248 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 18 2013 *)

Prog

(Magma) I:=[24, 25, 599, 624, 30551, 31175, 747576, 778751]; [n le 8 select I[n] else 1248*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Crossrefs

Cf. A042197.

Sequence in context: A042190 A042192 A042194 * A042197 A042198 A002924

Adjacent sequences: A042193 A042194 A042195 * A042197 A042198 A042199

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved