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A199772
x-values in the solution to 17*x^2 - 16 = y^2.
5
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
1,2
COMMENTS
When are both n+1 and 17*n+1 perfect squares? This problem gives the equation 17*x^2-16=y^2.
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
EXAMPLE
a(7) = 66*41-1 = 2705.
MATHEMATICA
LinearRecurrence[{0, 0, 66, 0, 0, -1}, {1, 4, 25, 41, 260, 1649}, 50]
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Nov 10 2011
EXTENSIONS
More terms from T. D. Noe, Nov 10 2011
STATUS
approved