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%I #27 Mar 30 2023 04:12:49
%S 0,0,0,3,4,5,12,14,16,27,30,33,48,52,56,75,80,85,108,114,120,147,154,
%T 161,192,200,208,243,252,261,300,310,320,363,374,385,432,444,456,507,
%U 520,533,588,602,616,675,690,705,768,784,800,867,884,901,972,990
%N a(n) = n*floor(n/3).
%C For n = 0, 1, 2, 4, 8, 49, 98, 676, 1352, 9409, 18818, 131044, 262088, 1825201, 3650402, ... a(n) is a square.
%H Bruno Berselli, <a href="/A242669/b242669.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 G.f.: x^3*(3 + x + x^2 + x^3)/((1 - x)^3*(1 + x + x^2)^2).
%F a(3m) = A033428(m), a(3m+1) = A049451(m), a(3m+2) = A045944(m).
%F Sum_{n>=3} (-1)^(n+1)/a(n) = 9/4 + Pi^2/36 - Pi/(2*sqrt(3)) - 2*log(2). - _Amiram Eldar_, Mar 30 2023
%t Table[n Floor[n/3], {n, 0, 60}]
%o (Magma) [n*Floor(n/3): n in [0..60]];
%o (Sage) [n*floor(n/3) for n in (0..60)];
%o (PARI) a(n)=n\3*n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A000290 (n^2), A010762 (floor(n/2)*floor(n/3)), A093353 (n*floor(n/2)), A213033 (n*floor(n/2)*floor(n/3)), A233035 (n*floor(n/4)).
%Y Cf. A033428, A045944, A049451.
%Y Cf. A002264 (floor(n/3)).
%K nonn,easy
%O 0,4
%A _Bruno Berselli_, Jul 01 2014
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