A213030 - OEIS

%I #16 Feb 20 2024 03:31:52

%S 0,0,1,3,3,8,12,12,21,27,27,40,48,48,65,75,75,96,108,108,133,147,147,

%T 176,192,192,225,243,243,280,300,300,341,363,363,408,432,432,481,507,

%U 507,560,588,588,645,675,675,736,768,768,833,867,867,936,972

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

%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 a(n) = a(n-1)+2*a(n-3)-2*a(n-4)-a(n-6)+a(n-7).

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

%t a[n_] := Floor[2*n/3]^2 - Floor[n/3]^2

%t Table[a[n], {n, 0, 60}]    (* A213030 *)

%t LinearRecurrence[{1,0,2,-2,0,-1,1},{0,0,1,3,3,8,12},60] (* _Harvey P. Dale_, Jul 06 2021 *)

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Jun 05 2012