%I #14 Dec 09 2023 02:18:02
%S 1,1,2,3,8,16,44,106,297,793,2259,6322,18212,52240,151818,440855,
%T 1288842,3767952,11058157,32452285,95467258
%N Number of free linear polycubes of size n, identifying rotations and reflections and avoiding the eight corner-connected neighbors.
%C Linear polycubes have two end points with one neighbor, the remaining cubes all have two neighbors.
%C When a cube [x,y,z] is in the polycube then neither of the eight cubes [x+-1,y+-1,z+-1] can be in the polycube.
%e The polycubes for n <= 5 are:
%e n=1:
%e 0,0,0
%e n=2:
%e 0,0,0; 0,0,1
%e n=3:
%e 0,0,0; 0,0,1; 0,0,2
%e 0,0,0; 0,0,1; 0,1,0
%e n=4:
%e 0,0,0; 0,0,1; 0,0,2; 0,0,3
%e 0,0,0; 0,0,1; 0,0,2; 0,1,0
%e 0,0,0; 0,0,1; 0,1,1; 0,1,2
%e n=5:
%e 0,0,0; 0,0,1; 0,0,2; 0,0,3; 0,0,4
%e 0,0,0; 0,0,1; 0,0,2; 0,0,3; 0,1,0
%e 0,0,0; 0,0,1; 0,0,2; 0,1,0; 0,1,2
%e 0,0,0; 0,0,1; 0,0,2; 0,1,0; 0,2,0
%e 0,0,0; 0,0,1; 0,0,2; 0,1,0; 1,0,2
%e 0,0,0; 0,0,1; 0,0,2; 0,1,2; 0,1,3
%e 0,0,0; 0,0,1; 0,1,1; 0,1,2; 0,2,2
%e 0,0,0; 0,0,1; 0,1,1; 0,2,1; 0,2,2
%Y Cf. A363203 (linear and avoiding at [0,0,+-2], [0,+-2,0], and [+-2,0,0]).
%K nonn,more
%O 1,3
%A _Joerg Arndt_ and _Márk Péter Légrádi_, May 21 2023
%E a(19)-a(21) from _Joerg Arndt_, Dec 09 2023