A199772 x-values in the solution to 17*x^2 - 16 = y^2.

1, 4, 25, 41, 260, 1649, 2705, 17156, 108809, 178489, 1132036, 7179745, 11777569, 74697220, 473754361, 777141065, 4928884484, 31260608081, 51279532721, 325231678724, 2062726378985, 3383672018521, 21460361911300, 136108680404929, 223271073689665

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*41-1 = 2705.
		

Links

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

Crossrefs

Cf. A199773, A199774, A199798.

Programs

Mathematica

LinearRecurrence[{0,0,66,0,0,-1}, {1,4,25,41,260,1649}, 50]

PARI

Vec(-x*(x-1)*(x^4+5*x^3+30*x^2+5*x+1)/(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)=1, a(2)=4, a(3)=25, a(4)=41, a(5)=260, a(6)=1649.

G.f.: -x*(x-1)*(x^4+5*x^3+30*x^2+5*x+1) / (x^6-66*x^3+1). - Colin Barker, Sep 01 2013

Extensions

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