A226695 Pell equation solutions (32*b(n))^2 - 41*(5*a(n))^2 = -1 with b(n) := A226694(n), n>=0.

1, 4097, 16789505, 68803387393, 281956264747009, 1155456704129855489, 4735061291567883046913, 19404280017388480596393985, 79518734776196701916139503617, 325867755708574067063859089428481, 1335405983375001750630992632338411521

Offset

0,2

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 (4098,-1)

Formula

a(n) = S(n,4098)- S(n-1,4098), n>=0, with the Chebyshev S-polynomials (A049310).

O.g.f.: (1-x)/(1 - 4098*x + x^2).

a(n) = 4098*a(n-1) - a(n-2), n >= 1, a(-1) = 1, a(0) =1.

Example

Pell n=0: 32^2 - 41*5^2 = -1.
Pell n=1: (32*4099)^2 - 41*(5*4097)^2 = -1.

Mathematica

LinearRecurrence[{4098, -1}, {1, 4097}, 20] (* Harvey P. Dale, May 17 2015 *)

Crossrefs

Cf. A049310, A226694.

Sequence in context: A013960 A036090 A123094 * A031562 A345507 A346357

Adjacent sequences: A226692 A226693 A226694 * A226696 A226697 A226698

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 20 2013

Status

approved