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 A173653 #30 Jun 02 2025 09:50:03
%S A173653 0,0,0,0,1,3,6,10,16,24,34,46,60,76,95,117,142,170,202,238,278,322,
%T A173653 370,422,479,541,608,680,758,842,932,1028,1130,1238,1353,1475,1604,
%U A173653 1740,1884,2036,2196,2364,2540,2724,2917,3119,3330,3550,3780,4020,4270,4530,4800
%N A173653 Partial sums of floor(n^2/10) (A056865).
%H A173653 Mircea Merca, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Merca/merca3.html">Inequalities and Identities Involving Sums of Integer Functions</a> J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
%H A173653 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,0,0,1,-3,3,-1).
%F A173653 a(n) = Sum_{k=0..n} floor(k^2/10).
%F A173653 a(n) = a(n-10)+(n-5)^2+n-1 , n>9.
%F A173653 From _R. J. Mathar_, Nov 24 2010: (Start)
%F A173653 G.f.: x^4*(1+x^4) / ( (1+x)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^4 ).
%F A173653 a(n)= +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-10) -3*a(n-11) +3*a(n-12) -a(n-13). (End)
%F A173653 a(n) = floor((2*n^3+3*n^2-26*n+24)/60) + floor((n+1)/10) - floor((n+3)/10). - _Hoang Xuan Thanh_, Jun 02 2025
%e A173653 a(9) = 0+0+0+0+1+2+3+4+6+8 = 24.
%t A173653 Accumulate[Floor[Range[0,50]^2/10]] (* _Harvey P. Dale_, May 31 2012 *)
%o A173653 (PARI) a(n)=(2*n^3+3*n^2-26*n)\/60 - ((n+3)%10<2) \\ _Charles R Greathouse IV_, Jun 02 2025
%Y A173653 Cf. A056865
%K A173653 nonn,easy
%O A173653 0,6
%A A173653 _Mircea Merca_, Nov 24 2010