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%I #15 Jul 31 2015 12:35:33
%S 54,13824,354294,3538944,21093750,90699264,311299254,905969664,
%T 2324522934,5400000000,11575379574,23219011584,44049458934,
%U 79692609024,138396093750,231928233984,376690901814,595077871104,917112404214
%N Product of three solutions of the Diophantine equation x^2 - y^2 = z^3.
%C Parametric representation of the solution is (x,y,z) = (6n^3, 3n^3, 3n^2), thus getting a(n) = 54*n^8.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F a(n) = 54*n^8.
%F 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
%p A085482:=n->54*n^8; seq(A085482(n), n=1..50); # _Wesley Ivan Hurt_, Nov 26 2013
%t 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 *)
%Y Cf. A085409.
%K nonn,easy
%O 1,1
%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Aug 15 2003
%E More terms from _Ray Chandler_, Nov 06 2003
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