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 A090022 #24 Mar 11 2022 12:39:31
%S A090022 0,1,25,253,2065,15541,112825,804973,5692705,40071781,281367625,
%T A090022 1972955293,13823978545,96820307221,677949854425,4746473419213,
%U A090022 33228592555585,232613204977861,1628344491013225,11398619145204733
%N A090022 Number of distinct lines through the origin in the n-dimensional lattice of side length 6.
%C A090022 Equivalently, lattice points where the gcd of all the coordinates is 1.
%H A090022 Gennady Eremin, <a href="/A090022/b090022.txt">Table of n, a(n) for n = 0..500</a>
%F A090022 a(n) = 7^n - 4^n - 3^n + 1.
%F A090022 O.g.f.: 1/(-1+3*x) + 1/(-1+4*x) - 1/(-1+x) - 1/(-1+7*x). - _R. J. Mathar_, Feb 26 2008
%e A090022 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.
%t A090022 Table[7^n - 4^n - 3^n + 1, {n, 0, 25}]
%o A090022 (Python) [7**n-4**n-3**n+1 for n in range(20)] # _Gennady Eremin_, Mar 06 2022
%o A090022 (Magma) [7^n-4^n-3^n+1: n in [0..20]]; // _Wesley Ivan Hurt_, Mar 06 2022
%Y A090022 a(n) = T(n, 5) from A090030. Cf. A000225, A001047, A060867, A090020, A090021, A090023, A090024 are for dimension n with side lengths 1, 2, 3, 4, 5, 7, 8 respectively. A049691, A090025, A090026, A090027, A090028, A090029 are for side length k in 2, 3, 4, 5, 6, 7 dimensions.
%K A090022 easy,nonn
%O A090022 0,3
%A A090022 _Joshua Zucker_, Nov 20 2003