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%I #31 Mar 23 2024 08:05:02
%S 1,2,4,7,11,15,20,25,31,38,46,54,63,72,82,93,105,117,130,143,157,172,
%T 188,204,221,238,256,275,295,315,336,357,379,402,426,450,475,500,526,
%U 553,581,609,638,667,697,728,760,792,825,858,892,927,963,999,1036,1073
%N Floor(average of first n squares).
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,1,-2,1)
%F a(n) = floor((1/n)*(Sum_{i=1, ..., n} i^2) = floor( A000330(n)/n ).
%F a(n) = [(n + 1) * (2 * n + 1) / 6]. A171662(n) = a(-1 - n). - _Michael Somos_, Dec 14 2009
%F G.f.: -x*(1+x^3+x^4+x^2) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^3 ). - _R. J. Mathar_, Feb 20 2011
%F a(n) = floor(n/(1-e^(-3/n))). Also see related exponential formula in A171662 with symmetry as above. - _Richard R. Forberg_, Jun 22 2013
%e a(4) = floor((1 + 4 + 9 + 16)/4) = 7.
%t Table[Floor[Mean[Range[n]^2]],{n,60}] (* _Harvey P. Dale_, Jun 19 2023 *)
%o (PARI) {a(n) = n++; (2 * n^2 - n) \ 6} /* _Michael Somos_, Dec 14 2009 */
%Y Cf. A000330, A171662.
%K easy,nonn
%O 1,2
%A _Joseph L. Pe_, Dec 10 2002
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