A334087 Draw the lines with equations y=kx (k=1..n) on the R^2/Z^2 square flat torus. a(n) is the number of intersection points.

0, 0, 1, 2, 5, 9, 17, 25, 39, 55, 77, 99, 131, 165, 211, 257, 311, 369, 443, 517, 609, 705, 813, 921, 1051, 1185, 1339, 1493, 1665, 1843, 2049, 2255, 2491, 2735, 2999, 3263, 3551, 3845, 4175, 4505, 4859, 5221, 5623, 6025, 6469, 6923, 7401, 7879, 8403, 8935, 9509

Offset

0,4

Comments

It appears that the second differences of this sequence yield A326305.

Links

Table of n, a(n) for n=0..50.

Luc Rousseau, Illustration of the fact that a(7) = 25

Prog

(PARI)
f(i, j, c, d)=my(L=List(), x, y); x=(d-c)/(j-i); if(max(c/i, d/j)<=x&&x<min((c+1)/i, (d+1)/j), y=(d*i-c*j)/(j-i); listinsert(L, [x, y], 1)); L
g(i, j)=my(c, d, L, S=Set()); for(c=0, i-1, for(d=c+1, j-1, L=f(i, j, c, d); S=setunion(S, Set(L)))); S
h(n)=my(i, j, S=Set()); for(i=1, n-1, for(j=i+1, n, S=setunion(S, g(i, j)))); S
a(n)=(n>1)+#h(n)
for(n=0, 60, print1(a(n), ", "))

Crossrefs

Cf. A326305.

Sequence in context: A123324 A167887 A023603 * A308760 A342854 A062492

Adjacent sequences: A334084 A334085 A334086 * A334088 A334089 A334090

Keyword

nonn

Author

Luc Rousseau, Apr 15 2020

Status

approved