

A097730


Pell equation solutions (6*b(n))^2  37*a(n)^2 = 1 with b(n):=A097729(n), n>=0.


5



1, 145, 21169, 3090529, 451196065, 65871534961, 9616792908241, 1403985893068225, 204972323595052609, 29924555258984612689, 4368780095488158399985, 637811969386012141785121
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..461
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (146, 1).


FORMULA

a(n) = S(n, 2*73)  S(n1, 2*73) = T(2*n+1, sqrt(37)/sqrt(37), 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 Ttriangle.
a(n) = ((1)^n)*S(2*n, 12*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1x)/(1146*x+x^2).
a(n) = 146*a(n1)a(n2), n>1 ; a(0)=1, a(1)=145 . [Philippe Deléham, Nov 18 2008]


EXAMPLE

(x,y) = (6,1), (882,145), (128766,21169), ... give the positive integer solutions to x^2  37*y^2 =1.


MATHEMATICA

LinearRecurrence[{146, 1}, {1, 145}, 12] (* Ray Chandler, Aug 12 2015 *)


CROSSREFS

Cf. A097729 for S(n, 146).
Row 6 of array A188647.
Sequence in context: A031612 A226849 A018232 * A283520 A265439 A060720
Adjacent sequences: A097727 A097728 A097729 * A097731 A097732 A097733


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Aug 31 2004


STATUS

approved



