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A294017
Partial sums of A294016.
6
1, 5, 12, 26, 43, 73, 106, 154, 211, 285, 362, 472, 585, 719, 872, 1056, 1243, 1473, 1706, 1984, 2285, 2615, 2948, 3354, 3773, 4225, 4704, 5240, 5779, 6403, 7030, 7720, 8441, 9203, 9992, 10892, 11795, 12743, 13726, 14810, 15897, 17093, 18292, 19572, 20919, 22319, 23722, 25278, 26851, 28511, 30214, 32010, 33809
OFFSET
1,2
COMMENTS
a(n) is also the volume of another version of the pyramid with n levels (starting from the top) described in A245092. Both pyramids have the same top view and the same front view, but in this pyramid the volume in the n-th level is equal to A294016(n) instead of A024916(n).
FORMULA
a(n) = A175254(n) - A072481(n).
PROG
(Python)
from math import isqrt
def A294017(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)))//3-n*(n+1)*((n<<1)+1)//6 # Chai Wah Wu, Oct 22 2023
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 22 2017
STATUS
approved