A036487 a(n) = floor((n^3)/2).

0, 0, 4, 13, 32, 62, 108, 171, 256, 364, 500, 665, 864, 1098, 1372, 1687, 2048, 2456, 2916, 3429, 4000, 4630, 5324, 6083, 6912, 7812, 8788, 9841, 10976, 12194, 13500, 14895, 16384, 17968, 19652, 21437, 23328, 25326, 27436, 29659, 32000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Crossrefs

Cf. A033430 (bisection), A268201 (bisection).

Programs

Maple

[ seq(floor((n^3)/2), n=0..100) ];

Mathematica

A036487[n_]:=Floor[n^3/2]
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 *)

PARI

a(n)=n^3\2 \\ Charles R Greathouse IV, Jul 18 2014

Sage

[floor(n^3/2) for n in range(0,41)] # Zerinvary Lajos, Dec 02 2009

Formula

G.f. x^2*(4 + x + x^2)/((1 + x)*(1 - x)^4). - R. J. Mathar, Jan 29 2011

From Stefano Spezia, Sep 09 2022: (Start)

a(n) = ((-1)^n - 1 + 2*n^3)/4.

E.g.f.: (x*(1 + 3*x + x^2)*cosh(x) - (1 - x - 3*x^2 - x^3)*sinh(x))/2. (End)

Extensions

Corrupted b-file corrected by Michael De Vlieger, Jul 18 2014