A328366 a(n) is the surface area of the stepped pyramid with n levels described in A245092.

6, 20, 40, 70, 102, 150, 194, 256, 318, 394, 462, 566, 646, 750, 858, 984, 1088, 1238, 1354, 1518, 1666, 1826, 1966, 2182, 2344, 2532, 2720, 2944, 3120, 3384, 3572, 3826, 4054, 4298, 4534, 4860, 5084, 5356, 5624, 5964, 6212, 6572, 6832, 7176, 7512, 7840, 8124, 8564, 8874, 9260, 9608, 10012

Offset: 1

Author

Omar E. Pol, Oct 26 2019

Keywords

• nonn

Examples

			For n = 1 the first level of the stepped pyramid is a cube, so a(1) = 6.
		

Crossrefs

Cf. A000217, A002378, A013661, A024916, A045943, A046092, A153485, A175254 (volume), A196020, A235791, A236104, A237270, A237271, A237591, A237593, A245092, A262626, A299692, A327329.

Programs

Mathematica

s=0;Do[s=s+4*DivisorSigma[1,n];t=2n(n+1);Print[(s/2)+t],{n,1,8000}] (* Metin Sariyar, Nov 20 2019 *)

Python

from math import isqrt
def A328366(n): return (n*(n+1)<<1)-(s:=isqrt(n))**2*(s+1)+sum((q:=n//k)*((k<<1)+q+1) for k in range(1,s+1)) # Chai Wah Wu, Oct 22 2023

Formula

a(n) = 4*A000217(n) + 2*A024916(n).

a(n) = 2*(A002378(n) + A327329(n)).

a(n) = 2*(A045943(n) + A153485(n)).

a(n) = A046092(n) + A327329(n).

a(n) = 2*A299692(n).

a(n) = c * n^2 + O(n*log(n)), where c = zeta(2) + 2 = 3.644934... . - Amiram Eldar, Mar 21 2024