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 A368032 #14 Dec 10 2023 15:15:44 %S A368032 1,1,1,2,3,7,11,20,34,65,113,197,315,488,685,1002,1409,2019,2679,3667, %T A368032 4837,6558,8474,11018,13786,17882,22431,28918,36411,46905,59183,76343, %U A368032 96372,123464,153738,193710,237629,294513,357010,436593 %N A368032 Number of free linear midpoint-free polycubes of size n, identifying rotations and reflections. %C A368032 Linear polycubes have two end points with one neighbor, the remaining cubes all have two neighbors. %C A368032 Midpoint-free means that no three cubes are in positions (x,y,z), (x+dx,y+dx,z+dz), and (x+2*dx,y+2*dx,z+2*dz). %e A368032 The polycubes for n <= 6 are: %e A368032 n=1: %e A368032 0,0,0 %e A368032 n=2: %e A368032 0,0,0; 0,0,1 %e A368032 n=3: %e A368032 0,0,0; 0,0,1; 0,1,0 %e A368032 n=4: %e A368032 0,0,0; 0,0,1; 0,1,0; 1,0,1 %e A368032 0,0,0; 0,0,1; 0,1,1; 0,1,2 %e A368032 n=5: %e A368032 0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,0,2 %e A368032 0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,1,0 %e A368032 0,0,0; 0,0,1; 0,1,1; 1,1,1; 1,1,2 %e A368032 n=6: %e A368032 0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,0,2; 1,1,0 %e A368032 0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,0,2; 1,1,2 %e A368032 0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,1,1; 1,1,2 %e A368032 0,0,0; 0,0,1; 0,1,1; 0,1,2; 1,1,2; 1,1,3 %e A368032 0,0,0; 0,0,1; 0,1,1; 0,1,2; 1,1,2; 1,2,2 %e A368032 0,0,0; 0,0,1; 0,1,1; 1,1,1; 1,1,2; 1,2,2 %e A368032 0,0,0; 0,0,1; 0,1,1; 1,1,1; 1,2,1; 1,2,2 %Y A368032 Cf. A368031. %K A368032 nonn %O A368032 1,4 %A A368032 _Joerg Arndt_, Dec 09 2023