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A085479
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Product of three solutions of the Diophantine equation x^3 - y^3 = z^2.
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2
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728, 93184, 1592136, 11927552, 56875000, 203793408, 599539304, 1526726656, 3482001432, 7280000000, 14186660488, 26085556224, 45680920376, 76741030912, 124385625000, 195421011968, 298726553944, 445696183296, 650738625992
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OFFSET
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1,1
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COMMENTS
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Parametric representation of the solution is (x,y,z) = (8n^2, 7n^2, 13n^3), thus getting a(n) = 728*n^7.
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LINKS
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FORMULA
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a(n) = 728*n^7.
G.f.: 728*x*(1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
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MATHEMATICA
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PROG
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(PARI) Vec(728*x*(1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6) / (1 - x)^8 + O(x^25)) \\ Colin Barker, Oct 25 2019
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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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Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Aug 15 2003
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EXTENSIONS
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STATUS
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approved
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