A281237 Solutions x to the negative Pell equation y^2 = 72*x^2 - 73728 with x,y >= 0.

32, 96, 544, 3168, 18464, 107616, 627232, 3655776, 21307424, 124188768, 723825184, 4218762336, 24588748832, 143313730656, 835293635104, 4868448079968, 28375394844704, 165383920988256, 963928131084832, 5618184865520736, 32745181062039584, 190852901506716768

Offset

1,1

Comments

The corresponding values of y are in A281238.

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) = -8*sqrt(2)*((4-3*sqrt(2))*(3+2*sqrt(2))^n - (3-2*sqrt(2))^n*(4+3*sqrt(2))).

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

G.f.: 32*x*(1 - 3*x) / (1 - 6*x + x^2).

Example

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

Prog

(PARI) Vec(32*x*(1 - 3*x) / (1 - 6*x + x^2) + O(x^30))

Crossrefs

Cf. A281238.

Equals 32*A001541.

Sequence in context: A044600 A189884 A175165 * A197604 A287925 A039519

Adjacent sequences: A281234 A281235 A281236 * A281238 A281239 A281240

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2017

Status

approved