A041768 Numerators of continued fraction convergents to sqrt(405).

20, 161, 6460, 51841, 2080100, 16692641, 669785740, 5374978561, 215668928180, 1730726404001, 69444725088220, 557288527109761, 22360985809478660, 179445175002939041, 7200167985927040300, 57780789062419261441, 2318431730482697497940, 18605234632923999244961

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,322,0,-1).

Formula

G.f.: -(x^3-20*x^2-161*x-20) / ((x^2-18*x+1)*(x^2+18*x+1)). - Vincenzo Librandi, Nov 08 2013, simplified by Colin Barker, Dec 28 2013

a(n) = 322*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 08 2013, simplified by Colin Barker, Dec 28 2013

Mathematica

Numerator[Convergents[Sqrt[405], 30]] (* Vincenzo Librandi, Nov 07 2013 *)
CoefficientList[Series[(20 + 161 x + 6460 x^2 + 51841 x^3 + 6460 x^4 - 161 x^5 + 20 x^6 - x^7)/(1 - 103682 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 08 2013 *)
LinearRecurrence[{0, 322, 0, -1}, {20, 161, 6460, 51841}, 20] (* Harvey P. Dale, Apr 28 2022 *)

Prog

(Magma) I:=[20, 161, 6460, 51841, 2080100, 16692641, 669785740, 5374978561]; [n le 8 select I[n] else 103682*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 08 2013

Crossrefs

Cf. A041769, A040384.

Sequence in context: A126515 A118676 A067534 * A221870 A289181 A056114

Adjacent sequences: A041765 A041766 A041767 * A041769 A041770 A041771

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 28 2013

Status

approved