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

%I

%S 728,93184,1592136,11927552,56875000,203793408,599539304,1526726656,

%T 3482001432,7280000000,14186660488,26085556224,45680920376,

%U 76741030912,124385625000,195421011968,298726553944,445696183296,650738625992

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

%C Parametric representation of the solution is (x,y,z) = (8n^2, 7n^2, 13n^3), thus getting a(n) = 728*n^7.

%H Harvey P. Dale, <a href="/A085479/b085479.txt">Table of n, a(n) for n = 1..1000</a>

%H <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 a(n) = 728*n^7.

%F From _Colin Barker_, Oct 25 2019: (Start)

%F 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 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 (End)

%t 728*Range[20]^7 (* _Harvey P. Dale_, May 27 2012 *)

%o (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 Cf. A001015 (n^7), A085377.

%K nonn,easy

%O 1,1

%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Aug 15 2003

%E More terms from _Matthew Conroy_, Jan 16 2006

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Last modified December 6 08:53 EST 2019. Contains 329788 sequences. (Running on oeis4.)