A085482 Product of three solutions of the Diophantine equation x^2 - y^2 = z^3.

54, 13824, 354294, 3538944, 21093750, 90699264, 311299254, 905969664, 2324522934, 5400000000, 11575379574, 23219011584, 44049458934, 79692609024, 138396093750, 231928233984, 376690901814, 595077871104, 917112404214

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) = (6n^3, 3n^3, 3n^2), thus getting a(n) = 54*n^8.

Links

• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Crossrefs

Cf. A085409.

Programs

Maple

A085482:=n->54*n^8; seq(A085482(n), n=1..50); # Wesley Ivan Hurt, Nov 26 2013

Mathematica

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 *)

Formula

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

Extensions

More terms from Ray Chandler, Nov 06 2003