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A042576
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Numerators of continued fraction convergents to sqrt(817).
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2
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28, 29, 57, 143, 200, 343, 19408, 19751, 39159, 98069, 137228, 235297, 13313860, 13549157, 26863017, 67275191, 94138208, 161413399, 9133288552, 9294701951, 18427990503, 46150682957, 64578673460
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OFFSET
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0,1
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 686, 0, 0, 0, 0, 0, -1).
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FORMULA
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G.f.: (28 +29*x +57*x^2 +143*x^3 +200*x^4 +343*x^5 +200*x^6 -143*x^7 +57*x^8 -29*x^9 +28*x^10 -x^11)/(1 -686*x^6 +x^12). - Vincenzo Librandi, Nov 28 2013
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MATHEMATICA
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Numerator[Convergents[Sqrt[817], 30]] (* or *) CoefficientList[Series[(28 + 29 x + 57 x^2 + 143 x^3 + 200 x^4 + 343 x^5 + 200 x^6 - 143 x^7 + 57 x^8 - 29 x^9 + 28 x^10 - x^11)/(1 - 686 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 686, 0, 0, 0, 0, 0, -1}, {28, 29, 57, 143, 200, 343, 19408, 19751, 39159, 98069, 137228, 235297}, 30] (* Harvey P. Dale, Jan 17 2017 *)
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PROG
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(Magma) I:=[28, 29, 57, 143, 200, 343, 19408, 19751, 39159, 98069, 137228, 235297]; [n le 12 select I[n] else 686*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 28 2013
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CROSSREFS
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KEYWORD
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nonn,cofr,frac,easy
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AUTHOR
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STATUS
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approved
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