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 A090021 #15 Mar 06 2022 09:01:28
%S A090021 0,1,21,175,1185,7471,45801,277495,1672545,10056991,60405081,
%T A090021 362615815,2176242705,13059083311,78359348361,470170570135,
%U A090021 2821066729665,16926530042431,101559568723641,609358576700455,3656154951181425
%N A090021 Number of distinct lines through the origin in the n-dimensional lattice of side length 5.
%C A090021 Equivalently, lattice points where the gcd of all the coordinates is 1.
%H A090021 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-47,72,-36).
%F A090021 a(n) = 6^n - 3^n - 2*2^n + 2.
%F A090021 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]
%e A090021 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.
%t A090021 Table[6^n - 3^n - 2*2^n + 2, {n, 0, 25}]
%t A090021 LinearRecurrence[{12,-47,72,-36},{0,1,21,175},30] (* _Harvey P. Dale_, Jul 18 2016 *)
%Y A090021 a(n) = T(n, 5) from A090030. Cf. A000225, A001047, A060867, A090020, A090022, A090023, A090024 are for dimension n with side lengths 1, 2, 3, 4, 6, 7, 8 respectively. A049691, A090025, A090026, A090027, A090028, A090029 are for side length k in 2, 3, 4, 5, 6, 7 dimensions.
%K A090021 easy,nonn
%O A090021 0,3
%A A090021 _Joshua Zucker_, Nov 19 2003