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 A348096 #12 Oct 05 2021 02:56:37
%S A348096 0,0,1,0,0,1,1,0,1,3,1,0,8,5,1,2,39,14,2,0,187,31,4,0,880,66,4,0,4109,
%T A348096 142,12,2,19274,310,7,0,90965,694,19,0,432545,1445,15,0
%N A348096 Array A(n,s) read by rows: the free n-polysticks of the square lattice with symmetry group of order 2^s.
%C A348096 The array has 4 columns for symmetry groups of order 1, 2, 4 and 8 (subgroups of D_8).
%C A348096 Polysticks with group order 1 have no symmetry. Polysticks with group order 2 have either a mirror line (parallel to edges or along a diagonal of the lattice) or a rotation axis of order 2 (180-degree rotation). Polysticks of group order 4 have two orthogonal mirror lines and the 180-degree rotation. Polysticks of group order 8 have in addition a rotation axis or order 4 (90-degree rotations), i.e. the full symmetry of the square.
%F A348096 Sum_{s=0..3} A(n,s) = A019988(n).
%F A348096 8*A(n,0) + 4*A(n,1) + 2*A(n,2) + A(n,3) = A096267(n).
%F A348096 A(n,3) = 0 if n is not a multiple of 4.
%e A348096 The array starts
%e A348096 0 0 1 0
%e A348096 0 1 1 0
%e A348096 1 3 1 0
%e A348096 8 5 1 2
%e A348096 39 14 2 0
%e A348096 187 31 4 0
%e A348096 880 66 4 0
%e A348096 4109 142 12 2
%e A348096 19274 310 7 0
%e A348096 90965 694 19 0
%e A348096 A(4,3)=2 counts the fully-symmetric unit square and the cross.
%Y A348096 Cf. A019988 (row sums), A096267 (fixed polysticks).
%K A348096 tabf,nonn,more
%O A348096 1,10
%A A348096 _R. J. Mathar_, Sep 30 2021
%E A348096 Row n=11 added.- _R. J. Mathar_, Oct 05 2021