A307169 First class of all proper positive solutions y1(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.

4, 65, 1036, 16511, 263140, 4193729, 66836524, 1065190655, 16976213956, 270554232641, 4311891508300, 68719709900159, 1095203466894244, 17454535760407745, 278177368699629676, 4433383363433667071, 70655956446239043460, 1126061919776391028289, 17946334759976017409164

Offset

1,1

Comments

The corresponding x1 solutions are given in A307168.

For details see A307168.

Links

Table of n, a(n) for n=1..19.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (16,-1).

Formula

G.f.: x*(4 + x)/(1 - 16*x + x^2).

a(n) = -S(n, 16) + 20*S(n-1, 16) for n >= 1, with S(n,16) = A077412(n).

a(n) = sqrt((A307168(n)^2 - 9)/7) for n >= 1.

Crossrefs

Cf. A077412, A307168.

Sequence in context: A278547 A293562 A331577 * A335176 A307185 A206500

Adjacent sequences: A307166 A307167 A307168 * A307170 A307171 A307172

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 27 2019

Status

approved