OFFSET

0,4

COMMENTS

a(n) is the number of circles centered at (0,0) that pass through grid points of the hexagonal lattice that intersect the interior of an interval n < x < n+1 on the x-axis.

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 0..10000

IBM Research, Circles on a triangular grid, Ponder This Challenge December 2023.

Hugo Pfoertner, Table of n, a(n) for n = 0..500000

PROG

(PARI) is_a003136(n) = !n || #qfbsolve(Qfb(1, 1, 1), n, 3);

for (k=0, 75, my (k1=k^2+1, k2=k^2+2*k, m=0); for (j=k1, k2, m+=is_a003136(j)); print1(m, ", "))

(Python)

from sympy import factorint

def A364443(n): return sum(1 for k in range(n**2+1, (n+1)**2) if not any(e&1 for p, e in factorint(k).items() if p % 3 == 2)) # Chai Wah Wu, Aug 07 2023

CROSSREFS

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Aug 05 2023

STATUS

approved