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Number of free linear polycubes of size n, identifying rotations and reflections and avoiding the eight corner-connected neighbors.
2

%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