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 A042704 Numerators of continued fraction convergents to sqrt(882). 2
 29, 30, 89, 297, 1871, 5910, 13691, 19601, 1150549, 1170150, 3490849, 11642697, 73347031, 231683790, 536714611, 768398401, 45103821869, 45872220270, 136848262409, 456417007497, 2875350307391, 9082467929670 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 20 23:53 EDT 2024. Contains 373535 sequences. (Running on oeis4.)