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A085479 Product of three solutions of the Diophantine equation x^3 - y^3 = z^2.

%I A085479 #18 Oct 25 2019 18:13:20
%S A085479 728,93184,1592136,11927552,56875000,203793408,599539304,1526726656,
%T A085479 3482001432,7280000000,14186660488,26085556224,45680920376,
%U A085479 76741030912,124385625000,195421011968,298726553944,445696183296,650738625992
%N A085479 Product of three solutions of the Diophantine equation x^3 - y^3 = z^2.
%C A085479 Parametric representation of the solution is (x,y,z) = (8n^2, 7n^2, 13n^3), thus getting a(n) = 728*n^7.
%H A085479 Harvey P. Dale, <a href="/A085479/b085479.txt">Table of n, a(n) for n = 1..1000</a>
%H A085479 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A085479 a(n) = 728*n^7.
%F A085479 From _Colin Barker_, Oct 25 2019: (Start)
%F A085479 G.f.: 728*x*(1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6) / (1 - x)^8.
%F A085479 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.
%F A085479 (End)
%t A085479 728*Range[20]^7 (* _Harvey P. Dale_, May 27 2012 *)
%o A085479 (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
%Y A085479 Cf. A001015 (n^7), A085377.
%K A085479 nonn,easy
%O A085479 1,1
%A A085479 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Aug 15 2003
%E A085479 More terms from _Matthew Conroy_, Jan 16 2006