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A237254
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Values of x in the solutions to x^2 - 5xy + y^2 + 5 = 0, where 0 < x < y.
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4
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1, 2, 3, 9, 14, 43, 67, 206, 321, 987, 1538, 4729, 7369, 22658, 35307, 108561, 169166, 520147, 810523, 2492174, 3883449, 11940723, 18606722, 57211441, 89150161, 274116482, 427144083, 1313370969, 2046570254, 6292738363, 9805707187, 30150320846, 46981965681
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OFFSET
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1,2
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COMMENTS
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The corresponding values of y are given by a(n+2).
Also the solutions to 21x^2-20 is a perfect square. - Jaimal Ichharam, Jul 13 2014
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LINKS
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FORMULA
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a(n) = 5*a(n-2)-a(n-4).
G.f.: -x*(x-1)*(x^2+3*x+1) / (x^4-5*x^2+1).
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EXAMPLE
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9 is in the sequence because (x, y) = (9, 43) is a solution to x^2 - 5xy + y^2 + 5 = 0.
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MAPLE
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coeftayl( -x*(x-1)*(x^2+3*x+1) / (x^4-5*x^2+1), x=0, n);
end proc:
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MATHEMATICA
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Rest[CoefficientList[Series[- x (x - 1) (x^2 + 3 x + 1)/(x^4 - 5 x^2 + 1), {x, 0, 40}], x]] (* Vincenzo Librandi, Jul 01 2014 *)
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PROG
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(PARI) Vec(-x*(x-1)*(x^2+3*x+1)/(x^4-5*x^2+1) + O(x^100))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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