OFFSET
1,1
COMMENTS
a(n) is also the volume of a stepped pyramid with n levels which is another version of the stepped pyramid described in A244050. Both pyramids have the same top view and the same front view, that is to say externally both pyramids are equal, but this pyramid with n levels contains a central chamber whose volume is 4*A072481(n). For more information about the central chamber see the diagrams in A294629.
a(n) is the number of unit cubes of the pyramid with n levels.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..2000
EXAMPLE
Illustration of the top view of the pyramid with 16 levels and 4224 unit cubes:
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MAPLE
with(numtheory): seq(sum(sum(8*(sigma(j)-j+(1/2)), j=1..k), k=1..n), n=1..50); # Muniru A Asiru, Mar 04 2018
MATHEMATICA
f[n_] := 8 (DivisorSigma[1, n] - n) + 4; Accumulate@ Accumulate@ Array[f, 48] (* Robert G. Wilson v, Dec 12 2017 *)
PROG
(GAP) List([1..50], n->Sum([1..n], m->Sum([1..m], k->8*(Sigma(k)-k+(1/2))))); # Muniru A Asiru, Mar 04 2018
(Python)
from math import isqrt
def A294630(n): return ((((s:=isqrt(n))**2*(s+1)*((s+1)*((s<<1)+1)-6*(n+1))>>1) + sum((q:=n//k)*(-k*(q+1)*(3*k+(q<<1)+1)+3*(n+1)*((k<<1)+q+1)) for k in range(1, s+1))<<2)-(n*(n+1)*((n<<1)+1)<<1))//3 # Chai Wah Wu, Nov 01 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 05 2017
STATUS
approved