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A041891
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Denominators of continued fraction convergents to sqrt(467).
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2
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1, 1, 2, 3, 5, 18, 59, 1257, 3830, 12747, 16577, 29324, 45901, 75225, 3205351, 3280576, 6485927, 9766503, 16252430, 58523793, 191823809, 4086823782, 12452295155, 41443709247, 53896004402, 95339713649, 149235718051, 244575431700, 10421403849451, 10665979281151
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3251252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
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FORMULA
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G.f.: -(x^26 -x^25 +2*x^24 -3*x^23 +5*x^22 -18*x^21 +59*x^20 -1257*x^19 +3830*x^18 -12747*x^17 +16577*x^16 -29324*x^15 +45901*x^14 -75225*x^13 -45901*x^12 -29324*x^11 -16577*x^10 -12747*x^9 -3830*x^8 -1257*x^7 -59*x^6 -18*x^5 -5*x^4 -3*x^3 -2*x^2 -x -1)/(x^28 -3251252*x^14 +1). - Vincenzo Librandi, Dec 26 2013
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MATHEMATICA
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Denominator[Convergents[Sqrt[467], 30]] (* Harvey P. Dale, Nov 01 2011 *)
CoefficientList[Series[-(x^26 - x^25 + 2 x^24 - 3 x^23 + 5 x^22 - 18 x^21 + 59 x^20 - 1257 x^19 + 3830 x^18 - 12747 x^17 + 16577 x^16 - 29324 x^15 + 45901 x^14 - 75225 x^13 - 45901 x^12 - 29324 x^11 - 16577 x^10 - 12747 x^9 - 3830 x^8 - 1257 x^7 - 59 x^6 - 18 x^5 - 5 x^4 - 3 x^3 - 2 x^2 - x - 1)/(x^28 - 3251252 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)
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PROG
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(Magma) I:=[1, 1, 2, 3, 5, 18, 59, 1257, 3830, 12747, 16577, 29324, 45901, 75225, 3205351, 3280576, 6485927, 9766503, 16252430, 58523793, 191823809, 4086823782, 12452295155, 41443709247, 53896004402, 95339713649, 149235718051, 244575431700]; [n le 28 select I[n] else 3251252*Self(n-14)-Self(n-28): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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