login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Partial sums of A334136.
3

%I #22 Oct 25 2023 12:18:02

%S 0,3,11,32,56,116,164,269,373,535,655,963,1131,1443,1779,2244,2532,

%T 3195,3555,4353,4993,5749,6277,7657,8401,9451,10491,12003,12843,14931,

%U 15891,17844,19380,21162,22794,25979,27347,29567,31695,35205,36885,40821,42669,46281,49713,52953,55161,60989,63725,68282

%N Partial sums of A334136.

%C 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 a(n) = A143128(n) - A024916(n).

%F a(n) = A256533(n) - A175254(n). - _Omar E. Pol_, Apr 29 2020

%e 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 (PARI) a(n) = sum(k=1, n, (k-1)*sigma(k)); \\ _Michel Marcus_, Apr 19 2020

%o (Python)

%o from math import isqrt

%o 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 Cf. A000203, A024916, A064987, A143128, A175254, A237593, A244580, A256533, A334136.

%K nonn

%O 1,2

%A _Omar E. Pol_, Apr 19 2020