A281239 Solutions x to the negative Pell equation y^2 = 72*x^2 - 83232 with x,y >= 0.

34, 38, 66, 102, 162, 358, 578, 934, 2082, 3366, 5442, 12134, 19618, 31718, 70722, 114342, 184866, 412198, 666434, 1077478, 2402466, 3884262, 6280002, 14002598, 22639138, 36602534, 81613122, 131950566, 213335202, 475676134, 769064258, 1243408678, 2772443682

Offset

1,1

Comments

The corresponding values of y are in A281240.

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

Example

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

Prog

(PARI) Vec(2*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. A281240.

Equals (1/4)* A281241.

Sequence in context: A345510 A300155 A250738 * A295750 A141699 A296096

Adjacent sequences: A281236 A281237 A281238 * A281240 A281241 A281242

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2017

Status

approved