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A078618 a(n) = floor(average of first n cubes).

%I A078618 #21 Aug 22 2024 20:51:08
%S A078618 1,4,12,25,45,73,112,162,225,302,396,507,637,787,960,1156,1377,1624,
%T A078618 1900,2205,2541,2909,3312,3750,4225,4738,5292,5887,6525,7207,7936,
%U A078618 8712,9537,10412,11340,12321,13357,14449,15600,16810,18081,19414,20812,22275
%N A078618 a(n) = floor(average of first n cubes).
%H A078618 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).
%F A078618 a(n) = floor((1/n)*(Sum_{i=1..n} i^3)) = floor(n*(n+1)^2/4).
%F A078618 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 A078618 a(3) = floor((1 + 8 + 27)/3) = 12.
%p A078618 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 A078618 s = 0; a = {}; For[i = 1, i <= 100, i++, s = s + i^3; a = Append[a, Floor[(1/i) s]]]; a
%o A078618 (PARI) a(n)=n*(n^2+2*n+1)\4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A078618 Cf. A000537.
%K A078618 easy,nonn
%O A078618 1,2
%A A078618 _Joseph L. Pe_, Dec 10 2002