This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090024 #18 Mar 12 2022 07:57:42
%S A090024 0,1,45,571,5841,55651,515025,4702531,42649281,385447171,3476958705,
%T A090024 31332052291,282184860321,2540643522691,22870684139985,
%U A090024 205860600134851,1852867557848961,16676418630942211,150090820212050865
%N A090024 Number of distinct lines through the origin in the n-dimensional lattice of side length 8.
%C A090024 Equivalently, lattice points where the gcd of all the coordinates is 1.
%H A090024 Gennady Eremin, <a href="/A090024/b090024.txt">Table of n, a(n) for n = 0..500</a>
%H A090024 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (20,-140,430,-579,270).
%F A090024 a(n) = 9^n - 5^n - 3^n - 2^n + 2.
%F A090024 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]
%e A090024 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 A090024 Table[9^n - 5^n - 3^n - 2^n + 2, {n, 0, 20}]
%o A090024 (Python)
%o A090024 [9**n-5**n-3**n-2**n+2 for n in range(30)] # _Gennady Eremin_, Mar 12 2022
%Y A090024 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 A090024 easy,nonn
%O A090024 0,3
%A A090024 _Joshua Zucker_, Nov 20 2003