A199798 y-values in the solution to 17*x^2 + 16 = y^2.

4, 13, 21, 132, 837, 1373, 8708, 55229, 90597, 574596, 3644277, 5978029, 37914628, 240467053, 394459317, 2501790852, 15867181221, 26028336893, 165080281604, 1046993493533, 1717475775621, 10892796795012, 69085703391957, 113327372854093, 718759508189188

Offset: 1

Author

Sture Sjöstedt, Nov 10 2011

Keywords

• nonn
• easy

Comments

When are both n-1 and 17*n-1 perfect squares? This problem gives the equation 17*x^2+16=y^2.

Examples

			a(7)=66*132-4=8708.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,66,0,0,-1).

Crossrefs

Cf. A199774, A199772, A199773.

Programs

Mathematica

LinearRecurrence[{0,0,66,0,0,-1}, {4,13,21,132,837,1373}, 50]

PARI

Vec(-x*(13*x^5+21*x^4+132*x^3-21*x^2-13*x-4)/(x^6-66*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Formula

a(n) = 66*a(n-3) - a(n-6), a(1)=4, a(2)=13, a(3)=21, a(4)=132, a(5)=837, a(6)=1373.

G.f.: -x*(13*x^5+21*x^4+132*x^3-21*x^2-13*x-4) / (x^6-66*x^3+1). - Colin Barker, Sep 01 2013

Extensions

More terms from T. D. Noe, Nov 10 2011