A226702 Positive solutions y/5 of the Pell equation x^2 - 61*y^2 = -4.

1, 1522, 2318005, 3530320093, 5376675183634, 8188672774354489, 12471343258666703113, 18993847594276614486610, 28927617414740025196403917, 44056742328801464097508678981, 67098389639147215080480521684146

Offset

0,2

Comments

The proper and improper positive solutions of the Pell equation x^2 - 61*y^2 = -4 are x = 39*A226701(n) and y = 5*a(n), n >= 1.

References

T. Nagell, Introduction to Number Theory, Chelsea Publishing Company, New York, 1964, ch. Vi, 58., p. 204-212.

Links

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

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (1523,-1).

Formula

a(n) = S(n,1523) - S(n-1,1523), n >= 0, with the Chebyshev S-polynomials (A049310), where S(-1,x) = 0.

O.g.f.: (1 - x)/(1 - 1523*x + x^2).

a(n) = 1523*a(n-1) - a(n-2), n>=1, a(-1) = 1, a(0) = 1.

Mathematica

LinearRecurrence[{1523, -1}, {1, 1522}, 20] (* Harvey P. Dale, Aug 03 2014 *)

Crossrefs

Cf. A226701, A049310.

Sequence in context: A103962 A263983 A031756 * A318791 A087867 A073104

Adjacent sequences: A226699 A226700 A226701 * A226703 A226704 A226705

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 27 2013

Status

approved