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A098245
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Chebyshev polynomials S(n,227).
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5
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1, 227, 51528, 11696629, 2655083255, 602692202256, 136808474828857, 31054921093948283, 7049330279851431384, 1600166918605180975885, 363230841193096230094511, 82451800783914239050478112
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OFFSET
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0,2
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COMMENTS
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Used for all positive integer solutions of Pell equation x^2 - 229*y^2 = -4. See A098246 with A098247.
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LINKS
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FORMULA
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a(n) = S(n, 227) = U(n, 227/2) = S(2*n+1, sqrt(229))/sqrt(229) with S(n, x) = U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x) = 0 = U(-1, x).
a(n) = 227*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=227; a(-1):=0.
a(n) = (ap^(n+1) - am^(n+1))/(ap-am) with ap := (227+15*sqrt(229))/2 and am := (227-15*sqrt(229))/2 = 1/ap.
G.f.: 1/(1-227*x+x^2).
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MATHEMATICA
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CoefficientList[Series[1/(1 - 227*x + x^2), {x, 0, 15}], x] (* Wesley Ivan Hurt, Feb 09 2017 *)
LinearRecurrence[{227, -1}, {1, 227}, 20] (* Harvey P. Dale, Jan 15 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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