OFFSET
0,3
COMMENTS
Equivalently, lattice points where the gcd of all the coordinates is 1.
LINKS
Gennady Eremin, Table of n, a(n) for n = 0..500
FORMULA
a(n) = 7^n - 4^n - 3^n + 1.
O.g.f.: 1/(-1+3*x) + 1/(-1+4*x) - 1/(-1+x) - 1/(-1+7*x). - R. J. Mathar, Feb 26 2008
EXAMPLE
a(2) = 25 because in 2D the lines have slope 0, 1/6, 5/6, 1/5, 2/5, 3/5, 4/5, 1/4, 3/4, 1/3, 2/3, 1/2, 1 and their reciprocals.
MATHEMATICA
Table[7^n - 4^n - 3^n + 1, {n, 0, 25}]
PROG
(Python) [7**n-4**n-3**n+1 for n in range(20)] # Gennady Eremin, Mar 06 2022
(Magma) [7^n-4^n-3^n+1: n in [0..20]]; // Wesley Ivan Hurt, Mar 06 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Joshua Zucker, Nov 20 2003
STATUS
approved