A281238 Solutions y to the negative Pell equation y^2 = 72*x^2 - 73728 with x,y >= 0.

0, 768, 4608, 26880, 156672, 913152, 5322240, 31020288, 180799488, 1053776640, 6141860352, 35797385472, 208642452480, 1216057329408, 7087701523968, 41310151814400, 240773209362432, 1403329104360192, 8179201416798720, 47671879396432128, 277852074961794048

Offset

1,2

Comments

The corresponding values of x are in A281237.

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 (6,-1).

Formula

a(n) = 96*sqrt(2)*(-(3-2*sqrt(2))^n*(3+2*sqrt(2)) + (3-2*sqrt(2))*(3+2*sqrt(2))^n).

a(n) = 6*a(n-1) - a(n-2) for n>2.

G.f.: 768*x^2 / (1 - 6*x + x^2).

Example

768 is in the sequence because (x, y) = (96,768) is a solution to y^2 = 72*x^2 - 73728.

Prog

(PARI) concat(0, Vec(768*x^2 / (1 - 6*x + x^2) + O(x^30)))

Crossrefs

Cf. A281237.

Equals 768*A001109.

Sequence in context: A257414 A179668 A219317 * A268808 A183687 A269051

Adjacent sequences: A281235 A281236 A281237 * A281239 A281240 A281241

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2017

Status

approved