OFFSET
0,3
COMMENTS
Equivalently, lattice points where the gcd of all the coordinates is 1.
LINKS
Index entries for linear recurrences with constant coefficients, signature (12,-47,72,-36).
FORMULA
a(n) = 6^n - 3^n - 2*2^n + 2.
G.f.: -x*(30*x^2-9*x-1)/((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). [Colin Barker, Sep 04 2012]
EXAMPLE
a(2) = 21 because in 2D the lines have slope 0, 1/5, 2/5, 3/5, 4/5, 1/4, 3/4, 1/3, 2/3, 1/2, 1 and their reciprocals.
MATHEMATICA
Table[6^n - 3^n - 2*2^n + 2, {n, 0, 25}]
LinearRecurrence[{12, -47, 72, -36}, {0, 1, 21, 175}, 30] (* Harvey P. Dale, Jul 18 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Joshua Zucker, Nov 19 2003
STATUS
approved