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A098257 Chebyshev polynomials S(n,531). 2
1, 531, 281960, 149720229, 79501159639, 42214966048080, 22416067470370841, 11902889611800868491, 6320411967798790797880, 3356126852011546112805789, 1782097038006163187109076079, 946290171054420640808806592160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Used for all positive integer solutions of Pell equation x^2 - 533*y^2 = -4. See A098258 with A098259.

LINKS

Table of n, a(n) for n=0..11.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (531, -1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= S(n, 531)=U(n, 531/2)= S(2*n+1, sqrt(533))/sqrt(533) 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)=531*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=531; a(-1):=0.

a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (531+23*sqrt(533))/2 and am := (531-23*sqrt(533))/2 = 1/ap.

G.f.: 1/(1-531*x+x^2).

CROSSREFS

Sequence in context: A158367 A225937 A225936 * A174780 A191950 A048055

Adjacent sequences:  A098254 A098255 A098256 * A098258 A098259 A098260

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Sep 10 2004

STATUS

approved

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Last modified May 26 08:35 EDT 2017. Contains 287093 sequences.