A200409 The y-values in the solution to 19*x^2 - 18 = y^2.

1, 39, 571, 911, 13299, 194141, 309739, 4521621, 66007369, 105310349, 1537337841, 22442311319, 35805208921, 522690344319, 7630319841091, 12173665722791, 177713179730619, 2594286303659621, 4139010540540019, 60421958418066141, 882049712924430049

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

Vincenzo Librandi, Table of n, a(n) for n = 1..300

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)=39, a(3)=571, a(4)=911, a(5)=13299, a(6)=194141.

G.f.: x*(x+1)*(x^4 + 38*x^3 + 533*x^2 + 38*x + 1) / (x^6 - 340*x^3 + 1). - Colin Barker, Sep 01 2013

Example

a(7) = 340*911 - 1 = 309739.

Mathematica

LinearRecurrence[{0, 0, 340, 0, 0, -1}, {1, 39, 571, 911, 13299, 194141}, 50]

Prog

(Magma) I:=[1, 39, 571, 911, 13299, 194141]; [n le 6 select I[n] else 340*Self(n-3)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, Nov 18 2011
(PARI) Vec(x*(x+1)*(x^4+38*x^3+533*x^2+38*x+1)/(x^6-340*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Crossrefs

Cf. A200407, A199773, A199774, A199798.

Sequence in context: A193072 A077454 A142976 * A363836 A341565 A034187

Adjacent sequences: A200406 A200407 A200408 * A200410 A200411 A200412

Keyword

nonn,easy

Author

Sture Sjöstedt, Nov 17 2011

Status

approved