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

728, 93184, 1592136, 11927552, 56875000, 203793408, 599539304, 1526726656, 3482001432, 7280000000, 14186660488, 26085556224, 45680920376, 76741030912, 124385625000, 195421011968, 298726553944, 445696183296, 650738625992

Offset: 1

Author

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

Keywords

• nonn
• easy

Comments

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A001015 (n^7), A085377.

Programs

Mathematica

728*Range[20]^7 (* Harvey P. Dale, May 27 2012 *)

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

Formula

a(n) = 728*n^7.

From Colin Barker, Oct 25 2019: (Start)

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)

Extensions

More terms from Matthew Conroy, Jan 16 2006