A281241 Solutions x to the negative Pell equation y^2 = 72*x^2 - 1331712 with x,y >= 0.

136, 152, 264, 408, 648, 1432, 2312, 3736, 8328, 13464, 21768, 48536, 78472, 126872, 282888, 457368, 739464, 1648792, 2665736, 4309912, 9609864, 15537048, 25120008, 56010392, 90556552, 146410136, 326452488, 527802264, 853340808, 1902704536, 3076257032

Offset

1,1

Comments

The corresponding values of y are in A281242.

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.: 8*x*(17 + 19*x + 33*x^2 - 51*x^3 - 33*x^4 - 19*x^5) / (1 - 6*x^3 + x^6).

Example

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

Mathematica

Rest@ CoefficientList[Series[8 x (17 + 19 x + 33 x^2 - 51 x^3 - 33 x^4 - 19 x^5)/(1 - 6 x^3 + x^6), {x, 0, 31}], x] (* Michael De Vlieger, Jan 19 2017 *)

Prog

(PARI) Vec(8*x*(17 + 19*x + 33*x^2 - 51*x^3 - 33*x^4 - 19*x^5) / (1 - 6*x^3 + x^6) + O(x^40))

Crossrefs

Cf. A281242.

Equals 4*A281239.

Sequence in context: A365328 A269062 A270301 * A072884 A072889 A157714

Adjacent sequences: A281238 A281239 A281240 * A281242 A281243 A281244

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2017

Status

approved