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A098245 Chebyshev polynomials S(n,227). 5
1, 227, 51528, 11696629, 2655083255, 602692202256, 136808474828857, 31054921093948283, 7049330279851431384, 1600166918605180975885, 363230841193096230094511, 82451800783914239050478112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used for all positive integer solutions of Pell equation x^2 - 229*y^2 = -4. See A098246 with A098247.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..423

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (227, -1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

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).

MATHEMATICA

CoefficientList[Series[1/(1 - 227*x + x^2), {x, 0, 15}], x] (* Wesley Ivan Hurt, Feb 09 2017 *)

CROSSREFS

Sequence in context: A115998 A092324 A122976 * A190027 A090943 A252451

Adjacent sequences:  A098242 A098243 A098244 * A098246 A098247 A098248

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Sep 10 2004

STATUS

approved

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Last modified August 22 10:35 EDT 2017. Contains 290944 sequences.