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%I #18 Sep 10 2017 05:38:26
%S 1,4,12,25,45,73,112,162,225,302,396,507,637,787,960,1156,1377,1624,
%T 1900,2205,2541,2909,3312,3750,4225,4738,5292,5887,6525,7207,7936,
%U 8712,9537,10412,11340,12321,13357,14449,15600,16810,18081,19414,20812,22275
%N a(n) = floor(average of first n cubes).
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).
%F a(n) = floor((1/n)(Sum_{i=1..n} i^3) = floor(n*(n+1)^2/4).
%F G.f.: x*(1+x+x^4+3*x^2) / ( (1+x)*(x^2+1)*(x-1)^4 ). - _R. J. Mathar_, Feb 20 2011
%e a(3) = floor((1 + 8 + 27)/3) = 12.
%p ZL:=n->sum(i^3, i=1..n): a:=n->floor(numer(ZL(n))/n): seq(a(n), n=1..44); # _Zerinvary Lajos_, Mar 28 2007
%t s = 0; a = {}; For[i = 1, i <= 100, i++, s = s + i^3; a = Append[a, Floor[(1/i) s]]]; a
%o (PARI) a(n)=n*(n^2+2*n+1)\4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A000537.
%K easy,nonn
%O 1,2
%A _Joseph L. Pe_, Dec 10 2002
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