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A098291 Chebyshev polynomials S(n,731) + S(n-1,731) with Diophantine property. 2
1, 732, 535091, 391150789, 285930691668, 209014944458519, 152789638468485721, 111689016705518603532, 81644518422095630696171, 59682031277535200520297469, 43627483219359809484706753668 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(27*a(n))^2 - 733*b(n)^2 = -4 with b(n)=A098292(n) give all positive solutions of this Pell equation.

LINKS

Table of n, a(n) for n=0..10.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (731, -1).

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= S(n, 731) + S(n-1, 731) = S(2*n, sqrt(733)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 731)=A098263(n).

a(n)= (-2/27)*I*((-1)^n)*T(2*n+1, 27*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120.

G.f.: (1+x)/(1-731*x+x^2).

EXAMPLE

All positive solutions of Pell equation x^2 - 733*y^2 = -4 are

(27=27*1,1), (19764=27*732,730), (14447457=27*535091,533629),

(10561071303=27*391150789,390082069), ...

CROSSREFS

Sequence in context: A031705 A158396 A098263 * A255798 A044988 A178093

Adjacent sequences:  A098288 A098289 A098290 * A098292 A098293 A098294

KEYWORD

nonn,easy,changed

AUTHOR

Wolfdieter Lang, Sep 10 2004

STATUS

approved

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Last modified March 25 05:37 EDT 2017. Contains 284036 sequences.