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 A175827 #19 Sep 08 2022 08:45:52 %S A175827 0,1,2,3,5,8,12,17,24,33,43,56,71,88,108,131,157,186,219,256,296,341, %T A175827 390,443,501,564,632,705,784,869,959,1056,1159,1268,1384,1507,1637, %U A175827 1774,1919,2072,2232,2401,2578,2763,2957,3160,3372,3593,3824,4065,4315 %N A175827 Partial sums of ceiling(n^2/10). %C A175827 Partial sums of A036408. %H A175827 Vincenzo Librandi, <a href="/A175827/b175827.txt">Table of n, a(n) for n = 0..10000</a> %H A175827 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. %F A175827 a(n) = round((2*n+1)*(2*n^2 + 2*n + 27)/120). %F A175827 a(n) = floor((2*n^3 + 3*n^2 + 28*n + 36)/60). %F A175827 a(n) = ceiling((2*n^3 + 3*n^2 + 28*n - 9)/60). %F A175827 a(n) = a(n-10) + (n+1)*(n-10) + 43. %F A175827 From _R. J. Mathar_, Dec 06 2010: (Start) %F A175827 G.f.: x*(1 - x + x^3 + x^7 - x^9 + x^10) / ( (1+x)*(x^4 + x^3 + x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x-1)^4 ). %F A175827 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) %e A175827 a(10) = 0 + 1 + 1 + 1 + 2 + 3 + 4 + 5 + 7 + 9 + 10 = 43. %p A175827 seq(ceil((2*n^3+3*n^2+28*n-9)/60),n=0..50) %o A175827 (Magma) [Round((2*n+1)*(2*n^2+2*n+27)/120): n in [0..60]]; // _Vincenzo Librandi_, Jun 22 2011 %Y A175827 Cf. A175822, A175826. %K A175827 nonn %O A175827 0,3 %A A175827 _Mircea Merca_, Dec 05 2010