A363204 Number of free linear polycubes of size n, identifying rotations and reflections and avoiding the eight corner-connected neighbors.

1, 1, 2, 3, 8, 16, 44, 106, 297, 793, 2259, 6322, 18212, 52240, 151818, 440855, 1288842, 3767952, 11058157, 32452285, 95467258

Offset: 1

Author

Joerg Arndt and Márk Péter Légrádi, May 21 2023

Keywords

• nonn
• more

Comments

Linear polycubes have two end points with one neighbor, the remaining cubes all have two neighbors.

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.

Examples

			The polycubes for n <= 5 are:
n=1:
  0,0,0
n=2:
  0,0,0; 0,0,1
n=3:
  0,0,0; 0,0,1; 0,0,2
  0,0,0; 0,0,1; 0,1,0
n=4:
  0,0,0; 0,0,1; 0,0,2; 0,0,3
  0,0,0; 0,0,1; 0,0,2; 0,1,0
  0,0,0; 0,0,1; 0,1,1; 0,1,2
n=5:
  0,0,0; 0,0,1; 0,0,2; 0,0,3; 0,0,4
  0,0,0; 0,0,1; 0,0,2; 0,0,3; 0,1,0
  0,0,0; 0,0,1; 0,0,2; 0,1,0; 0,1,2
  0,0,0; 0,0,1; 0,0,2; 0,1,0; 0,2,0
  0,0,0; 0,0,1; 0,0,2; 0,1,0; 1,0,2
  0,0,0; 0,0,1; 0,0,2; 0,1,2; 0,1,3
  0,0,0; 0,0,1; 0,1,1; 0,1,2; 0,2,2
  0,0,0; 0,0,1; 0,1,1; 0,2,1; 0,2,2
		

Crossrefs

Cf. A363203 (linear and avoiding at [0,0,+-2], [0,+-2,0], and [+-2,0,0]).

Extensions

a(19)-a(21) from Joerg Arndt, Dec 09 2023