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A085482
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Product of three solutions of the Diophantine equation x^2 - y^2 = z^3.
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2
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54, 13824, 354294, 3538944, 21093750, 90699264, 311299254, 905969664, 2324522934, 5400000000, 11575379574, 23219011584, 44049458934, 79692609024, 138396093750, 231928233984, 376690901814, 595077871104, 917112404214
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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) = (6n^3, 3n^3, 3n^2), thus getting a(n) = 54*n^8.
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LINKS
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FORMULA
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a(n) = 54*n^8.
a(1)=54, a(2)=13824, a(3)=354294, a(4)=3538944, a(5)=21093750, a(6)=90699264, a(7)=311299254, a(8)=905969664, a(9)=2324522934, a(n)=9*a(n-1)- 36*a(n-2)+ 84*a(n-3)- 126*a(n-4)+126*a(n-5)- 84*a(n-6)+ 36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Jul 10 2013
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MAPLE
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MATHEMATICA
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54*Range[20]^8 (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {54, 13824, 354294, 3538944, 21093750, 90699264, 311299254, 905969664, 2324522934}, 20] (* Harvey P. Dale, Jul 10 2013 *)
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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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