A294017 Partial sums of A294016.

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

Author

Omar E. Pol, Oct 22 2017

Keywords

• nonn

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).

Crossrefs

Cf. A000203, A072481, A175254, A237593, A245092, A294015, A294016.

Programs

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

Formula

a(n) = A175254(n) - A072481(n).