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A263944
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Positive integers n such that (n+28)^3 - n^3 is a square.
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8
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28, 189, 959, 4648, 22323, 107009, 512764, 2456853, 11771543, 56400904, 270233019, 1294764233, 6203588188, 29723176749, 142412295599, 682338301288, 3269279210883, 15664057753169, 75051009555004, 359590990021893, 1722903940554503, 8254928712750664
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 6*a(n-1)-6*a(n-2)+a(n-3) for n>3.
G.f.: 7*x*(x-4)*(x+1) / ((x-1)*(x^2-5*x+1)).
a(n) = 7*(-2+(2^(-1-n)*((5-sqrt(21))^n*(-7+sqrt(21))+(5+sqrt(21))^n*(7+sqrt(21))))/sqrt(21)). - Colin Barker, Mar 05 2016
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EXAMPLE
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189 is in the sequence because (189+28)^3 - 189^3 = 1862^2.
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MATHEMATICA
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LinearRecurrence[{6, -6, 1}, {28, 189, 959}, 30] (* Harvey P. Dale, Dec 14 2016 *)
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PROG
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(PARI) Vec(7*x*(x-4)*(x+1)/((x-1)*(x^2-5*x+1)) + O(x^40))
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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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