A281235 Solutions x to the negative Pell equation y^2 = 72*x^2 - 332928 with x,y >= 0.

68, 76, 132, 204, 324, 716, 1156, 1868, 4164, 6732, 10884, 24268, 39236, 63436, 141444, 228684, 369732, 824396, 1332868, 2154956, 4804932, 7768524, 12560004, 28005196, 45278276, 73205068, 163226244, 263901132, 426670404, 951352268, 1538128516, 2486817356

Offset

1,1

Comments

The corresponding values of y are in A281236.

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

Example

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

Prog

(PARI) Vec(4*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. A281236.

Equals 4*A106527.

Sequence in context: A306113 A058980 A079703 * A097760 A180937 A024881

Adjacent sequences: A281232 A281233 A281234 * A281236 A281237 A281238

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2017

Status

approved