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
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Nov 10 2011
EXTENSIONS
More terms from T. D. Noe, Nov 10 2011
STATUS
approved