This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078617 #35 Aug 22 2024 20:51:44
%S A078617 1,2,4,7,11,15,20,25,31,38,46,54,63,72,82,93,105,117,130,143,157,172,
%T A078617 188,204,221,238,256,275,295,315,336,357,379,402,426,450,475,500,526,
%U A078617 553,581,609,638,667,697,728,760,792,825,858,892,927,963,999,1036,1073
%N A078617 Floor(average of first n squares).
%H A078617 <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 A078617 a(n) = floor((1/n)*(Sum_{i=1..n} i^2)) = floor( A000330(n)/n ).
%F A078617 a(n) = [(n + 1) * (2 * n + 1) / 6]. A171662(n) = a(-1 - n). - _Michael Somos_, Dec 14 2009
%F A078617 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 A078617 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 A078617 a(4) = floor((1 + 4 + 9 + 16)/4) = 7.
%t A078617 Table[Floor[Mean[Range[n]^2]],{n,60}] (* _Harvey P. Dale_, Jun 19 2023 *)
%o A078617 (PARI) {a(n) = n++; (2 * n^2 - n) \ 6} /* _Michael Somos_, Dec 14 2009 */
%Y A078617 Cf. A000290, A000330, A171662.
%K A078617 easy,nonn
%O A078617 1,2
%A A078617 _Joseph L. Pe_, Dec 10 2002