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 A175822 #41 Mar 17 2023 07:13:52 %S A175822 0,1,2,4,7,11,17,24,34,46,61,79,100,125,153,186,223,265,312,364,422, %T A175822 485,555,631,714,804,901,1006,1118,1239,1368,1506,1653,1809,1975,2150, %U A175822 2336,2532,2739,2957,3186,3427,3679,3944,4221,4511,4814,5130,5460,5803,6161 %N A175822 Partial sums of ceiling(n^2/7). %C A175822 Partial sums of A036405. %H A175822 Vincenzo Librandi, <a href="/A175822/b175822.txt">Table of n, a(n) for n = 0..10000</a> %H A175822 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 A175822 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,1,-3,3,-1). %F A175822 a(n) = round((2*n+1)*(n^2 + n + 12)/42). %F A175822 a(n) = floor((n+1)*(2*n^2 + n + 24)/42). %F A175822 a(n) = ceiling((2*n^3 + 3*n^2 + 25*n)/42). %F A175822 a(n) = a(n-7) + (n+1)*(n-7) + 24, n > 6. %F A175822 From _R. J. Mathar_, Dec 06 2010: (Start) %F A175822 G.f.: x*(1+x)*(x^2 - x + 1)*(x^4 - x^3 + x^2 - x + 1) / ( (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^4 ). %F A175822 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-7) - 3*a(n-8) + 3*a(n-9) - a(n-10). (End) %e A175822 a(7) = 0 + 1 + 1 + 2 + 3 + 4 + 6 + 7 = 24. %p A175822 seq(round((2*n+1)*(n^2+n+12)/42),n=0..50) %t A175822 Ceiling[Range[0,50]^2/7]//Accumulate (* _Harvey P. Dale_, Apr 12 2018 *) %o A175822 (Magma) [&+[Ceiling(k^2/7): k in [0..n]]: n in [0..50]]; // _Bruno Berselli_, Apr 26 2011 %o A175822 (PARI) a(n)=(n+1)*(2*n^2+n+24)\42 \\ _Charles R Greathouse IV_, Oct 16 2015 %Y A175822 Cf. A036405. %K A175822 nonn,easy %O A175822 0,3 %A A175822 _Mircea Merca_, Dec 05 2010