A042724 Numerators of continued fraction convergents to sqrt(892).

29, 30, 209, 448, 6481, 13410, 86941, 100351, 5907299, 6007650, 41953199, 89914048, 1300749871, 2691413790, 17449232611, 20140646401, 1185606723869, 1205747370270, 8420090945489, 18045929261248

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, 200702, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (29 +30*x +209*x^2 +448*x^3 +6481*x^4 +13410*x^5 +86941*x^6 +100351*x^7 +86941*x^8 -13410*x^9 +6481*x^10 -448*x^11 +209*x^12 -30*x^13 +29*x^14 -x^15)/(1 -200702*x^8 +x^16). - Vincenzo Librandi, Dec 02 2013

a(n) = 200702*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[892], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 209 x^2 + 448 x^3 + 6481 x^4 + 13410 x^5 + 86941 x^6 + 100351 x^7 + 86941 x^8 - 13410 x^9 + 6481 x^10 - 448 x^11 + 209 x^12 - 30 x^13 + 29 x^14 - x^15)/(1 - 200702 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 200702, 0, 0, 0, 0, 0, 0, 0, -1}, {29, 30, 209, 448, 6481, 13410, 86941, 100351, 5907299, 6007650, 41953199, 89914048, 1300749871, 2691413790, 17449232611, 20140646401}, 20] (* Harvey P. Dale, Jul 25 2016 *)

Prog

(Magma) I:=[29, 30, 209, 448, 6481, 13410, 86941, 100351, 5907299, 6007650, 41953199, 89914048, 1300749871, 2691413790, 17449232611, 20140646401]; [n le 16 select I[n] else 200702*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013

Crossrefs

Cf. A042725.

Sequence in context: A042720 A042718 A042722 * A042726 A042728 A042730

Adjacent sequences: A042721 A042722 A042723 * A042725 A042726 A042727

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved