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A263945
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Positive integers n such that (n+39)^3 - n^3 is a square.
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8
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26, 871, 59930, 1155895, 77814386, 1500376111, 101003038370, 1947487061455, 131101866015146, 2527836705417751, 170170121084646410, 3281130096145204615, 220880686066005050306, 4258904336959770197791, 286702960343553470676050, 5528054548243685571553375
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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) = a(n-1)+1298*a(n-2)-1298*a(n-3)-a(n-4)+a(n-5) for n>5.
G.f.: 13*x*(5*x^4+65*x^3-1947*x^2-65*x-2) / ((x-1)*(x^2-36*x-1)*(x^2+36*x-1)).
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EXAMPLE
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26 is in the sequence because (26+39)^3 - 26^3 = 507^2.
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MATHEMATICA
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LinearRecurrence[{1, 1298, -1298, -1, 1}, {26, 871, 59930, 1155895, 77814386}, 20] (* Harvey P. Dale, Mar 25 2020 *)
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PROG
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(PARI) Vec(13*x*(5*x^4+65*x^3-1947*x^2-65*x-2)/((x-1)*(x^2-36*x-1)*(x^2+36*x-1)) + O(x^30))
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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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