This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A036486 #44 Sep 09 2022 16:59:36
%S A036486 0,1,4,14,32,63,108,172,256,365,500,666,864,1099,1372,1688,2048,2457,
%T A036486 2916,3430,4000,4631,5324,6084,6912,7813,8788,9842,10976,12195,13500,
%U A036486 14896,16384,17969,19652,21438,23328,25327,27436,29660,32000,34461,37044
%N A036486 a(n) = ceiling((n^3)/2).
%C A036486 a(n) is the number of compositions of even natural numbers into 3 parts < n. For example, a(2)=4 because compositions of even natural numbers into 3 parts < 2 are (0,0,0), (0,1,1), (1,0,1), and (1,1,0). a(3)=14 because compositions of even natural numbers into 3 parts <= 3 - 1 = 2 are (0,0,0), (0,1,1), (1,0,1), (1,1,0), (0,0,2), (0,2,0), (2,0,0), (1,1,2),(1,2,1),(2,1,1),(0,2,2),(2,0,2),(2,2,0) and (2,2,2). - _Adi Dani_, Jun 05 2011
%C A036486 Also the number of balls in a body-centered lattice cube with n layers. - _K. G. Stier_, Dec 26 2012
%H A036486 Vincenzo Librandi, <a href="/A036486/b036486.txt">Table of n, a(n) for n = 0..1000</a>
%H A036486 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A036486 G.f.: x*(1+x+4*x^2) / ( (1+x)*(x-1)^4 ). - _R. J. Mathar_, Jun 06 2011
%F A036486 a(n) = (2*n^3 - (-1)^n + 1)/4. - _Bruno Berselli_, Jun 07 2011
%F A036486 a(n) = n^3 - A036487(n), where n^3 is the number of compositions of natural numbers into 3 parts < n. - _R. J. Mathar_, Jun 07 2011
%F A036486 a(n) = (n^3 + (n mod 2))/2. - _Wesley Ivan Hurt_, May 21 2014
%F A036486 E.g.f.: (x*(1 + 3*x + x^2)*cosh(x) + (1 + x + 3*x^2 + x^3)*sinh(x))/2. - _Stefano Spezia_, Sep 09 2022
%p A036486 [ seq(ceil((n^3)/2), n=0..100) ];
%p A036486 with (combinat):seq(count(Partition((n^3+1)), size=2), n=0..40); # _Zerinvary Lajos_, Mar 28 2008
%t A036486 Table[Ceiling[n^3/2], {n, 0, 40}] (* _Wesley Ivan Hurt_, May 21 2014 *)
%t A036486 LinearRecurrence[{3,-2,-2,3,-1},{0,1,4,14,32},50] (* _Harvey P. Dale_, Jan 14 2019 *)
%o A036486 (Magma) [(2*n^3-(-1)^n+1)/4: n in [0..40]]; // _Vincenzo Librandi_, Jun 07 2011
%o A036486 (PARI) a(n)=(2*n^3-(-1)^n+1)/4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A036486 Cf. A036487.
%K A036486 nonn,easy
%O A036486 0,3
%A A036486 _N. J. A. Sloane_, Dec 11 1999