A199773 y-values in the solution to 17*x^2 - 16 = y^2.

1, 16, 103, 169, 1072, 6799, 11153, 70736, 448631, 735929, 4667504, 29602847, 48560161, 307984528, 1953339271, 3204234697, 20322311344, 128890789039, 211430929841, 1340964564176, 8504838737303, 13951237134809, 88483338924272, 561190465872959, 920570219967553

Offset

1,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

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)=1, a(2)=16, a(3)=103, a(4)=169, a(5)=1072, a(6)=6799.

G.f.: x*(x+1)*(x^4+15*x^3+88*x^2+15*x+1) / (x^6-66*x^3+1). - Colin Barker, Sep 01 2013

Example

a(7) = 66*169-1 = 11153.

Mathematica

LinearRecurrence[{0, 0, 66, 0, 0, -1}, {1, 16, 103, 169, 1072, 6799}, 50]
CoefficientList[Series[(x + 1) (x^4 + 15 x^3 + 88 x^2 + 15 x + 1) / (x^6 - 66 x^3 + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 06 2016 *)

Prog

(PARI) Vec(x*(x+1)*(x^4+15*x^3+88*x^2+15*x+1)/(x^6-66*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013
(Magma) I:=[1, 16, 103, 169, 1072, 6799]; [n le 6 select I[n] else 66*Self(n-3)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, Jan 06 2016

Crossrefs

Cf. A199772, A199774, A199798.

Sequence in context: A253390 A264281 A240257 * A245872 A304505 A210687

Adjacent sequences: A199770 A199771 A199772 * A199774 A199775 A199776

Keyword

nonn,easy

Author

Sture Sjöstedt, Nov 10 2011

Extensions

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

Status

approved