A281242 Solutions y to the negative Pell equation y^2 = 72*x^2 - 1331712 with x,y >= 0.

0, 576, 1920, 3264, 5376, 12096, 19584, 31680, 70656, 114240, 184704, 411840, 665856, 1076544, 2400384, 3880896, 6274560, 13990464, 22619520, 36570816, 81542400, 131836224, 213150336, 475263936, 768397824, 1242331200, 2770041216, 4478550720, 7240836864

Offset

1,2

Comments

The corresponding values of x are in A281241.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

S. Vidhyalakshmi, V. Krithika, K. Agalya, On The Negative Pell Equation  y^2 = 72*x^2 - 8, International Journal of Emerging Technologies in Engineering Research (IJETER), Volume 4, Issue 2, February (2016).

Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-1).

Formula

a(n) = 6*a(n-3) - a(n-6) for n>6.

G.f.: 192*x^2*(3 + 10*x + 17*x^2 + 10*x^3 + 3*x^4) / (1 - 6*x^3 + x^6).

Example

576 is in the sequence because (x, y) = (152,576) is a solution to y^2 = 72*x^2 - 1331712.

Mathematica

Rest@ CoefficientList[Series[192 x^2*(3 + 10 x + 17 x^2 + 10 x^3 + 3 x^4)/(1 - 6 x^3 + x^6), {x, 0, 29}], x] (* Michael De Vlieger, Jan 19 2017 *)
LinearRecurrence[{0, 0, 6, 0, 0, -1}, {0, 576, 1920, 3264, 5376, 12096}, 30] (* Harvey P. Dale, Feb 22 2018 *)

Prog

(PARI) concat(0, Vec(192*x^2*(3 + 10*x + 17*x^2 + 10*x^3 + 3*x^4) / (1 - 6*x^3 + x^6) + O(x^40)))

Crossrefs

Cf. A281241.

Equals 2*A281236.

Sequence in context: A137484 A189990 A064254 * A067225 A325475 A268797

Adjacent sequences: A281239 A281240 A281241 * A281243 A281244 A281245

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2017

Status

approved