A041920 Numerators of continued fraction convergents to sqrt(482).

21, 22, 461, 483, 20747, 21230, 445347, 466577, 20041581, 20508158, 430204741, 450712899, 19360146499, 19810859398, 415577334459, 435388193857, 18701881476453, 19137269670310, 401447274882653, 420584544552963, 18065998146107099, 18486582690660062

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,966,0,0,0,-1).

Formula

G.f.: (21 +22*x +461*x^2 +483*x^3 +461*x^4 -22*x^5 +21*x^6 -x^7)/(1 -966*x^4 +x^8). - Vincenzo Librandi, Nov 12 2013

a(n) = 966*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[482], 30]] (* or *) CoefficientList[Series[(21 + 22 x + 461 x^2 + 483 x^3 + 461 x^4 - 22 x^5 + 21 x^6 - x^7)/(1 - 966 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)
LinearRecurrence[{0, 0, 0, 966, 0, 0, 0, -1}, {21, 22, 461, 483, 20747, 21230, 445347, 466577}, 30] (* Harvey P. Dale, May 28 2023 *)

Prog

(Magma) I:=[21, 22, 461, 483, 20747, 21230, 445347, 466577]; [n le 8 select I[n] else 966*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 12 2013

Crossrefs

Cf. A041921, A040460.

Sequence in context: A041918 A068325 A041219 * A041921 A041922 A104669

Adjacent sequences: A041917 A041918 A041919 * A041921 A041922 A041923

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms and second link corrected by Colin Barker, Dec 28 2013

Status

approved