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A098248 Chebyshev polynomials S(n,291). 3
1, 291, 84680, 24641589, 7170617719, 2086625114640, 607200737742521, 176693328057958971, 51417151264128318040, 14962214324533282590669, 4353952951287921105566639, 1266985346610460508437301280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used for all positive integer solutions of Pell equation x^2 - 293*y^2 = -4. See A098249 with A098250.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..405

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (291,-1).

FORMULA

a(n)= S(n, 291)=U(n, 291/2)= S(2*n+1, sqrt(293))/sqrt(293) 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)=291*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=291; a(-1):=0.

a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (291+17*sqrt(293))/2 and am := (291-17*sqrt(293))/2 = 1/ap.

G.f.: 1/(1-291*x+x^2).

MATHEMATICA

LinearRecurrence[{291, -1}, {1, 291}, 20] (* Harvey P. Dale, Dec 27 2015 *)

CROSSREFS

Sequence in context: A031695 A158254 A088892 * A185999 A048956 A043439

Adjacent sequences:  A098245 A098246 A098247 * A098249 A098250 A098251

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Sep 10 2004

STATUS

approved

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Last modified July 23 22:27 EDT 2017. Contains 289716 sequences.