A200407 The x-values in the solution to 19*x^2 - 18 = y^2.

1, 9, 131, 209, 3051, 44539, 71059, 1037331, 15143129, 24159851, 352689489, 5148619321, 8214278281, 119913388929, 1750515426011, 2792830455689, 40770199546371, 595170096224419, 949554140655979, 13861747932377211, 202356082200876449, 322845614992577171

Offset

1,2

Comments

When are both n+1 and 19*n+1 perfect squares? This gives the equation 19*x^2-18=y^2.

Links

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (0,0,340,0,0,-1).

Formula

a(n) = 340*a(n-3)+a(n-6), a(1)=1, a(2)=9, a(3)=131, a(4)=209, a(5)=3051, a(6)=44539.

G.f.: -x*(x-1)*(x^4+10*x^3+141*x^2+10*x+1) / (x^6-340*x^3+1). - Colin Barker, Sep 01 2013

Example

a(7)=340*209-1=71059.

Mathematica

LinearRecurrence[{0, 0, 340, 0, 0, -1}, {1, 9, 131, 209, 3051, 44539}, 50]

Prog

(PARI) Vec(-x*(x-1)*(x^4+10*x^3+141*x^2+10*x+1)/(x^6-340*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Crossrefs

Cf. A199773, A199774, A199798, A200409.

Sequence in context: A328270 A060944 A299596 * A194895 A112123 A282820

Adjacent sequences: A200404 A200405 A200406 * A200408 A200409 A200410

Keyword

nonn,easy

Author

Sture Sjöstedt, Nov 17 2011

Status

approved