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%I #14 Feb 20 2024 03:26:17
%S 0,1,3,5,12,16,20,33,39,45,64,72,80,105,115,125,156,168,180,217,231,
%T 245,288,304,320,369,387,405,460,480,500,561,583,605,672,696,720,793,
%U 819,845,924,952,980,1065,1095,1125,1216,1248,1280,1377,1411
%N a(n) = n^2 - floor(2n/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)*(x + 2*x^2 + 2*x^3 + 5*x^4)/((1 - x)^3*(1 + x + x^2)^2).
%t a[n_] := n^2 - Floor[2 n/3]^2
%t Table[a[n], {n, 0, 90}] (* A213036 *)
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Jun 06 2012