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

1,1

Comments

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

Links

Table of n, a(n) for n=1..25.

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A199774, A199772, A199773.

Sequence in context: A155095 A063219 A063121 * A153193 A304905 A043469

Adjacent sequences: A199795 A199796 A199797 * A199799 A199800 A199801

Keyword

nonn,easy

Author

Sture Sjöstedt, Nov 10 2011

Extensions

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

Status

approved