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%I #17 Sep 08 2022 08:44:36
%S 0,0,0,0,0,0,1,2,2,2,2,2,4,6,6,6,6,6,9,12,12,12,12,12,16,20,20,20,20,
%T 20,25,30,30,30,30,30,36,42,42,42,42,42,49,56,56,56,56,56,64,72,72,72,
%U 72,72,81,90,90,90,90,90,100
%N a(n) = floor(n/6)*ceiling(n/6).
%H Vincenzo Librandi, <a href="/A008737/b008737.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2, -2, 2, -2, 2, 0, -2, 2, -2, 2, -2, 1).
%F G.f.: x^6/((1-x)^3*(1+x)*(1+x^2+x^4)^2). - _G. C. Greubel_, Jul 30 2019
%t Table[Floor[n/6] Ceiling[n/6], {n, 0, 70}] (* _Vincenzo Librandi_, Dec 19 2016 *)
%o (Magma) [Floor(n/6)*Ceiling(n/6): n in [0..70]]; // _Vincenzo Librandi_, Dec 19 2016
%o (PARI) vector(70, n, n--; (n\6)*ceil(n/6)) \\ _G. C. Greubel_, Jul 30 2019
%o (Magma) [Floor(n/6)*Ceiling(n/6): n in [0..70]]; // _G. C. Greubel_, Jul 30 2019
%o (Sage) [floor(n/6)*ceil(n/6) for n in (0..70)] # _G. C. Greubel_, Jul 30 2019
%o (GAP) a:=[0,0,0,0,0,0,1,2,2,2,2,2];; for n in [13..70] do a[n]:=2*(a[n-1] -a[n-2]+a[n-3]-a[n-4]+a[n-5]-a[n-7]+a[n-8]-a[n-9]+a[n-10]-a[n-11]) + a[n-12]; od; a; # _G. C. Greubel_, Jul 30 2019
%K nonn
%O 0,8
%A _N. J. A. Sloane_
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