A294017 - OEIS

%I #22 Oct 23 2023 02:00:15

%S 1,5,12,26,43,73,106,154,211,285,362,472,585,719,872,1056,1243,1473,

%T 1706,1984,2285,2615,2948,3354,3773,4225,4704,5240,5779,6403,7030,

%U 7720,8441,9203,9992,10892,11795,12743,13726,14810,15897,17093,18292,19572,20919,22319,23722,25278,26851,28511,30214,32010,33809

%N Partial sums of A294016.

%C 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).

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

%o (Python)

%o from math import isqrt

%o 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

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

%K nonn

%O 1,2

%A _Omar E. Pol_, Oct 22 2017