A174768 y-values in the solution to x^2 - 26*y^2 = 1.

0, 10, 1020, 104030, 10610040, 1082120050, 110365635060, 11256212656070, 1148023325284080, 117087122966320090, 11941738519239365100, 1217940241839448920110, 124217962929104550486120, 12669014278526824700664130, 1292115238446807014917255140, 131783085307295788696859360150

Offset: 1

Author

Vincenzo Librandi, Apr 14 2010

Keywords

• nonn
• easy

Comments

The corresponding values of x of this Pell equation are in A099397.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (102,-1).

Crossrefs

Cf. A041041, A099397.

Programs

Magma

I:=[0, 10]; [n le 2 select I[n] else 102*Self(n-1)-Self(n-2): n in [1..20]];

Mathematica

LinearRecurrence[{102,-1}, {0,10}, 30]
a[ n_] := Fibonacci[2*n-2, 10]; (* Michael Somos, Oct 25 2022 *)

Formula

a(n) = 102*a(n-1)-a(n-2) with a(1)=0, a(2)=10.

G.f.: 10*x^2/(1-102*x+x^2).

a(n+1) = A041041(2*n-1). - Michael Somos, Oct 25 2022