%I
%S 0,1,45,571,5841,55651,515025,4702531,42649281,385447171,3476958705,
%T 31332052291,282184860321,2540643522691,22870684139985,
%U 205860600134851,1852867557848961,16676418630942211,150090820212050865
%N Number of distinct lines through the origin in the ndimensional lattice of side length 8.
%C Equivalently, lattice points where the gcd of all the coordinates is 1.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (20,140,430,579,270).
%F a(n) = 9^n  5^n  3^n  2^n + 2.
%F G.f.: x*(291*x^3189*x^2+25*x+1)/((x1)*(2*x1)*(3*x1)*(5*x1)*(9*x1)). [_Colin Barker_, Sep 04 2012]
%e 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.
%t Table[9^n  5^n  3^n  2^n + 2, {n, 0, 20}]
%Y a(n) = T(n, 5) from A090030. Cf. A000225, A001047, A060867, A090020, A090021, A090022, A090023 are for dimension n with side lengths 1, 2, 3, 4, 5, 6, 7 respectively. A049691, A090025, A090026, A090027, A090028, A090029 are for side length k in 2, 3, 4, 5, 6, 7 dimensions.
%K easy,nonn
%O 0,3
%A _Joshua Zucker_, Nov 20 2003
