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A097767 Pell equation solutions (11*b(n))^2 - 122*a(n)^2 = -1 with b(n):=A097766(n), n>=0. 4
1, 485, 235709, 114554089, 55673051545, 27056988496781, 13149640736384021, 6390698340894137425, 3105866244033814404529, 1509444603902092906463669, 733586971630173118726938605, 356521758767660233608385698361 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (486, -1).

FORMULA

a(n)= S(n, 2*243) - S(n-1, 2*243) = T(2*n+1, sqrt(122))/sqrt(122), with Chebyshev polynomials of the 2nd and first kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x); and A053120 for the T-triangle.

a(n)= ((-1)^n)*S(2*n, 22*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.

G.f.: (1-x)/(1-486*x+x^2).

a(n)=486*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=485 . [From Philippe Deléham, Nov 18 2008]

EXAMPLE

(x,y) = (11*1=11;1), (5357=11*487;485), (2603491=11*236681;235709), ... give the positive integer solutions to x^2 - 122*y^2 =-1.

MATHEMATICA

LinearRecurrence[{486, -1}, {1, 485}, 12] (* Ray Chandler, Aug 12 2015 *)

CROSSREFS

Cf. A097765 for S(n, 486).

Row 11 of array A188647.

Sequence in context: A031722 A031610 A156774 * A031520 A235525 A249227

Adjacent sequences:  A097764 A097765 A097766 * A097768 A097769 A097770

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 31 2004

STATUS

approved

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Last modified August 24 05:48 EDT 2017. Contains 291052 sequences.