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A041092
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Numerators of continued fraction convergents to sqrt(54).
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2
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7, 15, 22, 147, 169, 485, 6959, 14403, 21362, 142575, 163937, 470449, 6750223, 13970895, 20721118, 138297603, 159018721, 456335045, 6547709351, 13551753747, 20099463098, 134148532335, 154247995433
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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 (0,0,0,0,0,970,0,0,0,0,0,-1).
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FORMULA
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a(n) = 970*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+15*x^9-22*x^8+147*x^7-169*x^6-485*x^5-169*x^4-147*x^3-22*x^2-15*x-7)/((x^4-10*x^2+1)*(x^8+10*x^6+99*x^4+10*x^2+1)). [Colin Barker, Jul 18 2012]
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MATHEMATICA
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Numerator[Convergents[Sqrt[54], 30]] (* Harvey P. Dale, Jul 18 2013 *)
CoefficientList[Series[- (x^11 - 7 x^10 + 15 x^9 - 22 x^8 + 147 x^7 - 169 x^6 - 485 x^5 - 169 x^4 - 147 x^3 - 22 x^2 - 15 x - 7)/((x^4 - 10 x^2 + 1) (x^8 + 10 x^6 + 99 x^4 + 10 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 25 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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