A140466 a(n) = 4*A002088(n).

0, 4, 8, 16, 24, 40, 48, 72, 88, 112, 128, 168, 184, 232, 256, 288, 320, 384, 408, 480, 512, 560, 600, 688, 720, 800, 848, 920, 968, 1080, 1112, 1232, 1296, 1376, 1440, 1536, 1584, 1728, 1800, 1896, 1960, 2120, 2168, 2336, 2416, 2512, 2600, 2784, 2848, 3016, 3096

Offset: 0

Author

Ed Pegg Jr, Jun 29 2008

Keywords

• nonn

Comments

Number of distinct slopes in an n X n grid.

Links

• Al Zimmermann, Table of n, a(n) for n = 0..49999
• Achim Flammenkamp, Cube 3

Crossrefs

Cf. A002088.

Programs

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def A140466(n): # based on second formula in A018805
    if n == 0:
        return 0
    c, j = 0, 2
    k1 = n//j
    while k1 > 1:
        j2 = n//k1 + 1
        c += (j2-j)*(A140466(k1)//2-1)
        j, k1 = j2, n//j2
    return 2*(n*(n-1)-c+j) # Chai Wah Wu, Mar 25 2021