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A200407
The x-values in the solution to 19*x^2 - 18 = y^2.
1
1, 9, 131, 209, 3051, 44539, 71059, 1037331, 15143129, 24159851, 352689489, 5148619321, 8214278281, 119913388929, 1750515426011, 2792830455689, 40770199546371, 595170096224419, 949554140655979, 13861747932377211, 202356082200876449, 322845614992577171
OFFSET
1,2
COMMENTS
When are both n+1 and 19*n+1 perfect squares? This gives the equation 19*x^2-18=y^2.
FORMULA
a(n) = 340*a(n-3)+a(n-6), a(1)=1, a(2)=9, a(3)=131, a(4)=209, a(5)=3051, a(6)=44539.
G.f.: -x*(x-1)*(x^4+10*x^3+141*x^2+10*x+1) / (x^6-340*x^3+1). - Colin Barker, Sep 01 2013
EXAMPLE
a(7)=340*209-1=71059.
MATHEMATICA
LinearRecurrence[{0, 0, 340, 0, 0, -1}, {1, 9, 131, 209, 3051, 44539}, 50]
PROG
(PARI) Vec(-x*(x-1)*(x^4+10*x^3+141*x^2+10*x+1)/(x^6-340*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Nov 17 2011
STATUS
approved