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A240836
Numbers n such that n^3 = x*y*z where 2 <= x <= y <= z , n^3+1 = (x-1)*(y+1)*(z+1).
1
2, 12, 80, 546, 3740, 25632, 175682, 1204140, 8253296, 56568930, 387729212, 2657535552, 18215019650, 124847601996, 855718194320, 5865179758242, 40200540113372, 275538601035360, 1888569667134146, 12944449068903660, 88722573815191472, 608113567637436642
OFFSET
1,1
COMMENTS
Also, z/y approx = y/x approx = golden ratio.
FORMULA
a(n) = 2*F(2n)*F(2n-1) where F(n) are the Fibonacci numbers (A000045).
G.f.: 2*x*(1-2*x)/((1-x)*(1-7*x+x^2)). - Colin Barker, Apr 13 2014
a(n) = 2 * A081016(n-1). - Wesley Ivan Hurt, Apr 13 2014
EXAMPLE
546^3 = 338 * 546 * 882, 546^3 + 1 = 337 * 547 * 883.
25632^3 = 15842 * 25632 * 41472, 25632^3 + 1 = 15841 * 25633 * 41473.
MAPLE
with(combinat); A240836:=n->2*fibonacci(2*n)*fibonacci(2*n-1); seq(A240836(n), n=1..30); # Wesley Ivan Hurt, Apr 13 2014
MATHEMATICA
Table[2Fibonacci[2n]Fibonacci[2n-1], {n, 30}] (* Wesley Ivan Hurt, Apr 13 2014 *)
PROG
(PARI) vector(30, n, f=fibonacci; 2*f(2*n)*f(2*n-1)) \\ G. C. Greubel, Jul 15 2019
(Magma) F:=Fibonacci; [2*F(2*n)*F(2*n-1): n in [1..30]]; // G. C. Greubel, Jul 15 2019
(Sage) f=fibonacci; [2*f(2*n)*f(2*n-1) for n in (1..30)] # G. C. Greubel, Jul 15 2019
(GAP) F:=Fibonacci;; List([1..30], n-> 2*F(2*n)*F(2*n-1) ); # G. C. Greubel, Jul 15 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Naohiro Nomoto, Apr 12 2014
EXTENSIONS
More terms from Colin Barker, Apr 13 2014
STATUS
approved