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A033431 a(n) = 2*n^3. 20

%I

%S 0,2,16,54,128,250,432,686,1024,1458,2000,2662,3456,4394,5488,6750,

%T 8192,9826,11664,13718,16000,18522,21296,24334,27648,31250,35152,

%U 39366,43904,48778,54000,59582,65536,71874,78608,85750,93312,101306,109744,118638

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

%C Also the largest determinant of a 3 X 3 matrix with entries from {0..n}. - _Jud McCranie_, Aug 12 2001

%C 4*a(n) is a perfect cube.

%C The positive terms comprise the principal diagonal of the convolution array A213821. - _Clark Kimberling_, Jul 04 2012

%C Volume of a pyramid (square base) with side n and height 6*n. - _Wesley Ivan Hurt_, Aug 25 2014

%H Vincenzo Librandi, <a href="/A033431/b033431.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 G.f. 2*x*(1 + 4*x + x^2) / (1 - x)^4. - _R. J. Mathar_, Feb 04 2011

%F a(n) = 2*A000578(n). - _Omar E. Pol_, May 14 2008

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Wesley Ivan Hurt_, Aug 25 2014

%F a(n) = A002378(n)^2 - A002378(n^2). - _Bruno Berselli_, Oct 20 2016

%F E.g.f.: 2*x*(1 + 3*x + x^2)*exp(x). - _G. C. Greubel_, Jul 15 2017

%p seq(2*n^3, n=0..39); # _Nathaniel Johnston_, Jun 26 2011

%t 2 Range[0, 50]^3 (* _Wesley Ivan Hurt_, Aug 25 2014 *)

%o (MAGMA) [2*n^3: n in [0..30]]; // _Vincenzo Librandi_, Jun 26 2011

%o (PARI) a(n)=2*n^3 \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Cf. A000578, A002378, A033581, A117642, A213821.

%K nonn,easy

%O 0,2

%A _Jeff Burch_

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Last modified September 19 14:43 EDT 2019. Contains 327198 sequences. (Running on oeis4.)