A042704 Numerators of continued fraction convergents to sqrt(882).

29, 30, 89, 297, 1871, 5910, 13691, 19601, 1150549, 1170150, 3490849, 11642697, 73347031, 231683790, 536714611, 768398401, 45103821869, 45872220270, 136848262409, 456417007497, 2875350307391, 9082467929670

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,-1).

Formula

G.f.: (29 +30*x +89*x^2 +297*x^3 +1871*x^4 +5910*x^5 +13691*x^6 +19601*x^7 +13691*x^8 -5910*x^9 +1871*x^10 -297*x^11 +89*x^12 -30*x^13 +29*x^14 -x^15)/(1 -39202*x^8 +x^16). - Vincenzo Librandi, Dec 02 2013

a(n) = 39202*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[882], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 89 x^2 + 297 x^3 + 1871 x^4 + 5910 x^5 + 13691 x^6 + 19601 x^7 + 13691 x^8 - 5910 x^9 + 1871 x^10 - 297 x^11 + 89 x^12 - 30 x^13 + 29 x^14 - x^15)/(1 - 39202 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *)

Prog

(Magma) I:=[29, 30, 89, 297, 1871, 5910, 13691, 19601, 1150549, 1170150, 3490849, 11642697, 73347031, 231683790, 536714611, 768398401]; [n le 16 select I[n] else 39202*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013

Crossrefs

Cf. A042705.

Sequence in context: A042706 A042708 A042710 * A042702 A042714 A042716

Adjacent sequences: A042701 A042702 A042703 * A042705 A042706 A042707

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved