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 A332264 #22 Oct 25 2023 12:18:02 %S A332264 0,3,11,32,56,116,164,269,373,535,655,963,1131,1443,1779,2244,2532, %T A332264 3195,3555,4353,4993,5749,6277,7657,8401,9451,10491,12003,12843,14931, %U A332264 15891,17844,19380,21162,22794,25979,27347,29567,31695,35205,36885,40821,42669,46281,49713,52953,55161,60989,63725,68282 %N A332264 Partial sums of A334136. %C A332264 a(n) is also the volume after n-th step of the symmetric staircase described in A244580 except the volume of the base level. %F A332264 a(n) = A143128(n) - A024916(n). %F A332264 a(n) = A256533(n) - A175254(n). - _Omar E. Pol_, Apr 29 2020 %e A332264 For n = 4 the volume of the first four levels of the symmetric staircase described in A244580 is 47, since the structure contains 47 cubes. The volume of the base level is 15, since the base of the structure contains 15 cubes, so a(4) = 47 - 15 = 32. %o A332264 (PARI) a(n) = sum(k=1, n, (k-1)*sigma(k)); \\ _Michel Marcus_, Apr 19 2020 %o A332264 (Python) %o A332264 from math import isqrt %o A332264 def A332264(n): return (((s:=isqrt(n))**2*(s+1)*(6-(s+1)*((s<<1)+1))>>1)+sum((q:=n//k)*(k*(q+1)*(3*k+(q<<1)+1)-3*((k<<1)+q+1)) for k in range(1,s+1)))//6 # _Chai Wah Wu_, Oct 25 2023 %Y A332264 Cf. A000203, A024916, A064987, A143128, A175254, A237593, A244580, A256533, A334136. %K A332264 nonn %O A332264 1,2 %A A332264 _Omar E. Pol_, Apr 19 2020