A332264 Partial sums of A334136.

0, 3, 11, 32, 56, 116, 164, 269, 373, 535, 655, 963, 1131, 1443, 1779, 2244, 2532, 3195, 3555, 4353, 4993, 5749, 6277, 7657, 8401, 9451, 10491, 12003, 12843, 14931, 15891, 17844, 19380, 21162, 22794, 25979, 27347, 29567, 31695, 35205, 36885, 40821, 42669, 46281, 49713, 52953, 55161, 60989, 63725, 68282

Offset

1,2

Comments

a(n) is also the volume after n-th step of the symmetric staircase described in A244580 except the volume of the base level.

Links

Table of n, a(n) for n=1..50.

Formula

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

a(n) = A256533(n) - A175254(n). - Omar E. Pol, Apr 29 2020

Example

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.

Prog

(PARI) a(n) = sum(k=1, n, (k-1)*sigma(k)); \\ Michel Marcus, Apr 19 2020
(Python)
from math import isqrt
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

Crossrefs

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

Sequence in context: A076477 A319335 A104079 * A089620 A144335 A202091

Adjacent sequences: A332261 A332262 A332263 * A332265 A332266 A332267

Keyword

nonn

Author

Omar E. Pol, Apr 19 2020

Status

approved