A328366 - OEIS

%I #26 Mar 21 2024 08:36:00

%S 6,20,40,70,102,150,194,256,318,394,462,566,646,750,858,984,1088,1238,

%T 1354,1518,1666,1826,1966,2182,2344,2532,2720,2944,3120,3384,3572,

%U 3826,4054,4298,4534,4860,5084,5356,5624,5964,6212,6572,6832,7176,7512,7840,8124,8564,8874,9260,9608,10012

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

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

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

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

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

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

%F a(n) = c * n^2 + O(n*log(n)), where c = zeta(2) + 2 = 3.644934... . - _Amiram Eldar_, Mar 21 2024

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

%t 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 *)

%o (Python)

%o from math import isqrt

%o 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

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

%K nonn

%O 1,1

%A _Omar E. Pol_, Oct 26 2019