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 A042708 Numerators of continued fraction convergents to sqrt(884). 2
 29, 30, 89, 119, 327, 446, 1219, 1665, 97789, 99454, 296697, 396151, 1088999, 1485150, 4059299, 5544449, 325637341, 331181790, 988000921, 1319182711, 3626366343, 4945549054, 13517464451, 18463013505, 1084372247741, 1102835261246, 3290042770233, 4392878031479 (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 (0,0,0,0,0,0,0,3330,0,0,0,0,0,0,0,-1). FORMULA G.f.: -(x^15 -29*x^14 +30*x^13 -89*x^12 +119*x^11 -327*x^10 +446*x^9 -1219*x^8 -1665*x^7 -1219*x^6 -446*x^5 -327*x^4 -119*x^3 -89*x^2 -30*x -29) / (x^16 -3330*x^8 +1). - Colin Barker, Nov 09 2013 a(n) = 3330*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 02 2013 MATHEMATICA Numerator[Convergents[Sqrt[884], 30]] (* Harvey P. Dale, Nov 16 2011 *) CoefficientList[Series[-(x^15 - 29 x^14 + 30 x^13 - 89 x^12 + 119 x^11 - 327 x^10 + 446 x^9 - 1219 x^8 - 1665 x^7 - 1219 x^6 - 446 x^5 - 327 x^4 - 119 x^3 - 89 x^2 - 30 x - 29)/(x^16 - 3330 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 02 2013 *) PROG (Magma) I:=[29, 30, 89, 119, 327, 446, 1219, 1665, 97789, 99454, 296697, 396151, 1088999, 1485150, 4059299, 5544449]; [n le 16 select I[n] else 3330*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 02 2013 CROSSREFS Cf. A042709. Sequence in context: A042684 A042682 A042706 * A042710 A042704 A042702 Adjacent sequences: A042705 A042706 A042707 * A042709 A042710 A042711 KEYWORD nonn,cofr,frac,easy AUTHOR N. J. A. Sloane. EXTENSIONS More terms from Colin Barker, Nov 09 2013 STATUS approved

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Last modified June 21 20:04 EDT 2024. Contains 373559 sequences. (Running on oeis4.)