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A281234
Solutions y to the negative Pell equation y^2 = 72*x^2 - 288 with x,y >= 0.
1
0, 48, 288, 1680, 9792, 57072, 332640, 1938768, 11299968, 65861040, 383866272, 2237336592, 13040153280, 76003583088, 442981345248, 2581884488400, 15048325585152, 87708069022512, 511200088549920, 2979492462277008, 17365754685112128, 101215035648395760
OFFSET
1,2
COMMENTS
The corresponding values of x are in A003499.
LINKS
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).
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).
EXAMPLE
48 is in the sequence because (x, y) = (6,48) is a solution to y^2 = 72*x^2 - 288.
PROG
(PARI) concat(0, Vec(48*x^2 / (1 - 6*x + x^2) + O(x^25)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 18 2017
STATUS
approved