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%I #45 Sep 09 2022 19:25:55
%S 0,0,4,13,32,62,108,171,256,364,500,665,864,1098,1372,1687,2048,2456,
%T 2916,3429,4000,4630,5324,6083,6912,7812,8788,9841,10976,12194,13500,
%U 14895,16384,17968,19652,21437,23328,25326,27436,29659,32000
%N a(n) = floor((n^3)/2).
%H Enrique Pérez Herrero, <a href="/A036487/b036487.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F G.f. x^2*(4 + x + x^2)/((1 + x)*(1 - x)^4). - _R. J. Mathar_, Jan 29 2011
%F From _Stefano Spezia_, Sep 09 2022: (Start)
%F a(n) = ((-1)^n - 1 + 2*n^3)/4.
%F E.g.f.: (x*(1 + 3*x + x^2)*cosh(x) - (1 - x - 3*x^2 - x^3)*sinh(x))/2. (End)
%p [ seq(floor((n^3)/2), n=0..100) ];
%t A036487[n_]:=Floor[n^3/2]
%t Floor[Range[0,40]^3/2] (* or *) LinearRecurrence[{3,-2,-2,3,-1},{0,0,4,13,32},50] (* _Harvey P. Dale_, Jun 24 2018 *)
%o (Sage) [floor(n^3/2) for n in range(0,41)] # _Zerinvary Lajos_, Dec 02 2009
%o (PARI) a(n)=n^3\2 \\ _Charles R Greathouse IV_, Jul 18 2014
%Y Cf. A033430 (bisection), A268201 (bisection).
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E Corrupted b-file corrected by _Michael De Vlieger_, Jul 18 2014
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