A281240 Solutions y to the negative Pell equation y^2 = 72*x^2 - 83232 with x,y >= 0.

0, 144, 480, 816, 1344, 3024, 4896, 7920, 17664, 28560, 46176, 102960, 166464, 269136, 600096, 970224, 1568640, 3497616, 5654880, 9142704, 20385600, 32959056, 53287584, 118815984, 192099456, 310582800, 692510304, 1119637680, 1810209216, 4036245840

Offset

1,2

Comments

The corresponding values of x are in A281239.

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

Example

144 is in the sequence because (x, y) = (38,144) is a solution to y^2 = 72*x^2 - 83232.

Mathematica

LinearRecurrence[{0, 0, 6, 0, 0, -1}, {0, 144, 480, 816, 1344, 3024}, 40] (* Harvey P. Dale, Oct 19 2022 *)

Prog

(PARI) concat(0, Vec(48*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. A281239.

Sequence in context: A258382 A151820 A322905 * A014770 A131528 A262797

Adjacent sequences: A281237 A281238 A281239 * A281241 A281242 A281243

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2017

Status

approved