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 A031876 #27 Aug 23 2017 10:58:59 %S A031876 0,1,2,3,4,5,6,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43, %T A031876 45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99,102,105,108, %U A031876 111,114,117,120,123,126,129,132,135,138,141,144,147,150,153,156,160 %N A031876 a(n) = Sum_{k=0..n} floor(k^(1/3)). %D A031876 K. H. Rosen, Discrete Mathematics and Its Application, 6th Edition, McGraw-Hill, 2007, Ex. 26 of section 2.4. %H A031876 G. C. Greubel, <a href="/A031876/b031876.txt">Table of n, a(n) for n = 0..1000</a> %F A031876 a(0) = 0, a(1) = 1, a(n) = 2*a(n-1) - a(n-2) if n not a perfect cube, else a(n) = 2*a(n-1) - a(n-2) + 1 if n is a perfect cube. %F A031876 a(n) = -1/4*floor(n^(1/3))*(floor(n^(1/3))^3+2*floor(n^(1/3))^2+floor(n^(1/3))-4*(n+1)). - _John M. Campbell_, Mar 22 2016 %F A031876 G.f.: Sum_{k>=1} x^(k^3)/(1 - x)^2. - _Ilya Gutkovskiy_, Dec 22 2016 %F A031876 a(n) = (3/4)*n^(4/3) + O(n). - _Charles R Greathouse IV_, Aug 23 2017 %t A031876 Accumulate[Floor[Surd[Range[0,70],3]]] (* _Harvey P. Dale_, Nov 03 2013 *) %t A031876 Table[Sum[Floor[i^(1/3)], {i,0,n}], {n,0,50}] (* _G. C. Greubel_, Dec 22 2016 *) %o A031876 (PARI) a(n) = sum(k=1, n, sqrtnint(k, 3)); \\ _Michel Marcus_, Mar 12 2016 %o A031876 (PARI) a(n)=my(t=sqrtnint(n,3)); t*(4*n-t^3-2*t^2-t+4)/4 \\ _Charles R Greathouse IV_, Aug 23 2017 %Y A031876 Cf. A022554. %K A031876 nonn,easy %O A031876 0,3 %A A031876 Michel Tixier (tixier(AT)dyadel.net)