A393009 a(n) is the sum of mutual Manhattan distances of the A000328(n) distinct grid points (x_i,y_i) in a square lattice such that x_i^2 + y_i^2 <= n^2.

0, 16, 192, 1456, 5416, 19168, 44000, 87840, 176840, 330640, 581600, 896568, 1326544, 2092136, 3023816, 4352128, 5828984, 7922344, 10514024, 13923280, 18216176, 22709264, 29145424, 36121112, 44259112, 55376432, 67366040, 81514856, 96903152, 115237224, 137454408

Offset

1,2

Comments

The coordinates of the grid points are provided in the first A000328(n) terms of A305575 and A305576.

Comparison against A193452:

n a(n) m=A000328(n)

A193452(m)

1 16 5 16

2 192 13 188

3 1456 29 1442

4 5416 49 5398

5 19168 81 19062

6 44000 113 43900

Links

Table of n, a(n) for n=1..31.

Formula

a(n) == 0 (mod 8).

a(n) >= A193452(A000328(n)).

Crossrefs

Cf. A000328, A085463, A193452, A305575, A305576.

Cf. A393008 (similar in 3D).

Sequence in context: A302298 A305773 A317122 * A230832 A305590 A232426

Adjacent sequences: A393006 A393007 A393008 * A393010 A393011 A393012

Keyword

nonn

Author

Hugo Pfoertner, Feb 03 2026

Status

approved