A008130 - OEIS

%I #31 Feb 07 2024 09:36:29

%S 0,0,0,1,2,2,4,6,6,9,12,12,16,20,20,25,30,30,36,42,42,49,56,56,64,72,

%T 72,81,90,90,100,110,110,121,132,132,144,156,156,169,182,182,196,210,

%U 210,225,240,240,256,272,272,289

%N a(n) = floor(n/3)*ceiling(n/3).

%H Vincenzo Librandi, <a href="/A008130/b008130.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1)

%F From _R. J. Mathar_, Jan 27 2011: (Start)

%F a(n) = A002264(n)*A002264(n+2).

%F G.f. -x^3*(1+x) / ( (1+x+x^2)^2*(x-1)^3 ). (End)

%p A008130:=n->ceil(n/3)*floor(n/3); seq(A008130(n), n=0..60); # _Wesley Ivan Hurt_, Feb 01 2014

%t f[n_]:=Ceiling[n/3]*Floor[n/3];Table[f[n],{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 01 2010 *)

%t CoefficientList[Series[- x^3 (1 + x) / ((1 + x + x^2)^2 (x - 1)^3), {x, 0, 60}], x] (* _Vincenzo Librandi_, Jun 10 2013 *)

%t LinearRecurrence[{1,0,2,-2,0,-1,1},{0,0,0,1,2,2,4},60] (* _Harvey P. Dale_, Dec 31 2016 *)

%o (Magma) [Floor(n/3)*Ceiling(n/3): n in [0..60]]; // _Vincenzo Librandi_, Jun 10 2013

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_