

A085482


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


2



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

1,1


COMMENTS

Parametric representation of the solution is (x,y,z) = (6n^3, 3n^3, 3n^2), thus getting a(n) = 54*n^8.


LINKS

Table of n, a(n) for n=1..19.
Index entries for linear recurrences with constant coefficients, signature (9, 36, 84, 126, 126, 84, 36, 9, 1).


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(n1) 36*a(n2)+ 84*a(n3) 126*a(n4)+126*a(n5) 84*a(n6)+ 36*a(n7)9*a(n8)+a(n9).  Harvey P. Dale, Jul 10 2013


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 *)


CROSSREFS

Cf. A085409.
Sequence in context: A178633 A299949 A228607 * A084226 A071800 A093254
Adjacent sequences: A085479 A085480 A085481 * A085483 A085484 A085485


KEYWORD

nonn,easy


AUTHOR

Jun Mizuki (suzuki32(AT)sanken.osakau.ac.jp), Aug 15 2003


EXTENSIONS

More terms from Ray Chandler, Nov 06 2003


STATUS

approved



