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
Index entries for linear recurrences with constant coefficients, signature (20,-140,430,-579,270).
FORMULA
a(n) = 9^n - 5^n - 3^n - 2^n + 2.
G.f.: -x*(291*x^3-189*x^2+25*x+1)/((x-1)*(2*x-1)*(3*x-1)*(5*x-1)*(9*x-1)). [Colin Barker, Sep 04 2012]
EXAMPLE
a(2) = 45 because in 2D the lines have slope 0, 1/8, 3/8, 5/8, 7/8, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 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[9^n - 5^n - 3^n - 2^n + 2, {n, 0, 20}]
PROG
(Python)
[9**n-5**n-3**n-2**n+2 for n in range(30)] # Gennady Eremin, Mar 12 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Joshua Zucker, Nov 20 2003
STATUS
approved