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 A042381 Denominators of continued fraction convergents to sqrt(717). 2
 1, 1, 4, 9, 112, 121, 2048, 2169, 28076, 58321, 203039, 261360, 13793759, 14055119, 55959116, 125973351, 1567639328, 1693612679, 28665442192, 30359054871, 392974100644, 816307256159, 2841895869121, 3658203125280, 193068458383681, 196726661508961 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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, 0, 0, 0, 0, 13996798, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1). FORMULA G.f.: -(x^22 -x^21 +4*x^20 -9*x^19 +112*x^18 -121*x^17 +2048*x^16 -2169*x^15 +28076*x^14 -58321*x^13 +203039* x^12 -261360*x^11 -203039*x^10 -58321*x^9 -28076*x^8 -2169*x^7 -2048*x^6 -121*x^5 -112*x^4 -9*x^3 -4*x^2 -x -1)/(x^24 -13996798*x^12 +1). - Vincenzo Librandi, Jan 21 2014 a(n) = 13996798*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Jan 21 2014 MATHEMATICA Denominator[Convergents[Sqrt[717], 30]] (* Harvey P. Dale, Feb 12 2013 *) CoefficientList[Series[-(x^22 - x^21 + 4 x^20 - 9 x^19 + 112 x^18 - 121 x^17 + 2048 x^16 -2169 x^15 + 28076 x^14 - 58321 x^13 + 203039 x^12 - 261360 x^11 - 203039 x^10 - 58321 x^9 - 28076 x^8 - 2169 x^7 - 2048 x^6 - 121 x^5 - 112 x^4 - 9 x^3 - 4 x^2 - x - 1)/(x^24 - 13996798 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 21 2014 *) PROG (Magma) I:=[1, 1, 4, 9, 112, 121, 2048, 2169, 28076, 58321, 203039, 261360, 13793759, 14055119, 55959116, 125973351, 1567639328, 1693612679, 28665442192, 30359054871, 392974100644, 816307256159, 2841895869121, 3658203125280]; [n le 24 select I[n] else 13996798*Self(n-12)-Self(n-24): n in [1..30]]; // Vincenzo Librandi, Jan 21 2014 CROSSREFS Cf. A042380. Sequence in context: A117680 A042649 A324024 * A230743 A033294 A156317 Adjacent sequences: A042378 A042379 A042380 * A042382 A042383 A042384 KEYWORD nonn,frac,easy AUTHOR N. J. A. Sloane. EXTENSIONS More terms from Vincenzo Librandi, Jan 21 2014 STATUS approved

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Last modified September 24 17:02 EDT 2023. Contains 365579 sequences. (Running on oeis4.)