A281234 Solutions y to the negative Pell equation y^2 = 72*x^2 - 288 with x,y >= 0.

0, 48, 288, 1680, 9792, 57072, 332640, 1938768, 11299968, 65861040, 383866272, 2237336592, 13040153280, 76003583088, 442981345248, 2581884488400, 15048325585152, 87708069022512, 511200088549920, 2979492462277008, 17365754685112128, 101215035648395760

Offset: 1

Author

Colin Barker, Jan 18 2017

Keywords

• nonn
• easy

Comments

The corresponding values of x are in A003499.

Examples

			48 is in the sequence because (x, y) = (6,48) is a solution to y^2 = 72*x^2 - 288.
		

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).

Crossrefs

Cf. A001109, A003499, A077420, A280761.

Programs

PARI

concat(0, Vec(48*x^2 / (1 - 6*x + x^2) + O(x^25)))

Formula

G.f.: 48*x^2 / (1 - 6*x + x^2).

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

a(n) = 48*A001109(n-1).

a(n) = 6*sqrt(2)*(-(3 - 2*sqrt(2))^n*(3+2*sqrt(2)) + (3 - 2*sqrt(2))*(3 + 2*sqrt(2))^n).