A281236 Solutions y to the negative Pell equation y^2 = 72*x^2 - 332928 with x,y >= 0.

0, 288, 960, 1632, 2688, 6048, 9792, 15840, 35328, 57120, 92352, 205920, 332928, 538272, 1200192, 1940448, 3137280, 6995232, 11309760, 18285408, 40771200, 65918112, 106575168, 237631968, 384198912, 621165600, 1385020608, 2239275360, 3620418432, 8072491680

Offset

1,2

Comments

The corresponding values of x are in A281235.

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

Example

288 is in the sequence because (x, y) = (76, 288) is a solution to y^2 = 72*x^2 - 332928.

Mathematica

LinearRecurrence[{0, 0, 6, 0, 0, -1}, {0, 288, 960, 1632, 2688, 6048}, 30] (* Harvey P. Dale, Jul 10 2019 *)

Prog

(PARI) concat(0, Vec(96*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. A281235.

Equals 2*A281240.

Sequence in context: A292054 A250788 A179646 * A237369 A280936 A250871

Adjacent sequences: A281233 A281234 A281235 * A281237 A281238 A281239

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2017

Status

approved