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A016743 Even cubes: a(n) = (2*n)^3. 10

%I

%S 0,8,64,216,512,1000,1728,2744,4096,5832,8000,10648,13824,17576,21952,

%T 27000,32768,39304,46656,54872,64000,74088,85184,97336,110592,125000,

%U 140608,157464,175616,195112,216000,238328,262144,287496,314432

%N Even cubes: a(n) = (2*n)^3.

%C a(n) is also the number of non-degenerate triangles that can be drawn with vertices on a cross with n points on each branch. - _James P. B. Hall_, Nov 22 2019

%H Vincenzo Librandi, <a href="/A016743/b016743.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = (2*n)^3 = 8*n^3.

%F G.f.: x*(8+32*x+8*x^2)/(1-4*x+6*x^2-4*x^3+x^4). - _Colin Barker_, Jan 02 2012

%F E.g.f.: 8*x*(1 +3*x +x^2)*exp(x). - _G. C. Greubel_, Sep 15 2018

%F From _Amiram Eldar_, Oct 10 2020: (Start)

%F Sum_{n>=1} 1/a(n) = zeta(3)/8 (A276712).

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 3*zeta(3)/32. (End)

%p A016743:=n->(2*n)^3: seq(A016743(n), n=0..50); # _Wesley Ivan Hurt_, Sep 15 2018

%t Range[0, 78, 2]^3 (* _Alonso del Arte_, Apr 06 2013 *)

%o (MAGMA) [(2*n)^3: n in [0..50]]; // _Vincenzo Librandi_, Sep 05 2011

%o (PARI) a(n) = 8*n^3; \\ _Joerg Arndt_, Apr 07 2013

%Y Even bisection of A000578, cf. A016755.

%Y Cf. A016803 (even bisection), A016827 (odd bisection), A033581, A276712.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified April 18 12:45 EDT 2021. Contains 343088 sequences. (Running on oeis4.)