A042852 Numerators of continued fraction convergents to sqrt(957).

30, 31, 464, 959, 13890, 14849, 904830, 919679, 13780336, 28480351, 412505250, 440985601, 26871641310, 27312626911, 409248418064, 845809463039, 12250580900610, 13096390363649, 798034002719550, 811130393083199, 12153859505884336, 25118849404851871

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,29698,0,0,0,0,0,-1).

Formula

G.f.: (30 +31*x +464*x^2 +959*x^3 +13890*x^4 +14849*x^5 +13890*x^6 -959*x^7 +464*x^8 -31*x^9 +30*x^10 -x^11)/(1 -29698*x^6 +x^12). - Vincenzo Librandi, Dec 07 2013

a(n) = 29698*a(n-6) - a(n-12), - Vincenzo Librandi, Dec 07 2013

Mathematica

Numerator[Convergents[Sqrt[957], 30]] (* or *) CoefficientList[Series[(30 + 31 x + 464 x^2 + 959 x^3 + 13890 x^4 + 14849 x^5 + 13890 x^6 - 959 x^7 + 464 x^8 - 31 x^9 + 30 x^10 - x^11)/(1 - 29698 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 07 2013 *)

Prog

(Magma) I:=[ 30, 31, 464, 959, 13890, 14849, 904830, 919679, 13780336, 28480351, 412505250, 440985601]; [n le 12 select I[n] else 29698*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 07 2013

Crossrefs

Cf. A042853.

Sequence in context: A042846 A042848 A042850 * A042854 A268337 A042856

Adjacent sequences: A042849 A042850 A042851 * A042853 A042854 A042855

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 07 2013

Status

approved