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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.

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

Original entry on oeis.org

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

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 21 2023

Keywords

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

A368029 Number of free midpoint-free polycubes of size n, identifying rotations and reflections.

Original entry on oeis.org

1, 1, 1, 4, 5, 18, 33, 70, 110, 246, 526, 1144, 2366, 4689, 8597, 15168, 26367, 46696, 82428, 142991, 240609, 393640, 627305, 975760, 1474671, 2164515, 3084956, 4282222, 5810980, 7776373, 10351373, 13815334, 18556147, 25107905
Offset: 1

Views

Author

Joerg Arndt , Dec 08 2023

Keywords

Comments

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).

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; 0,1,0
n=4:
  0,0,0; 0,0,1; 0,1,0; 0,1,1
  0,0,0; 0,0,1; 0,1,0; 1,0,0
  0,0,0; 0,0,1; 0,1,0; 1,0,1
  0,0,0; 0,0,1; 0,1,1; 0,1,2
n=5:
  0,0,0; 0,0,1; 0,1,0; 0,1,1; 1,0,0
  0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,0,2
  0,0,0; 0,0,1; 0,1,0; 1,0,1; 1,1,0
  0,0,0; 0,0,1; 0,1,1; 0,1,2; 1,0,1
  0,0,0; 0,0,1; 0,1,1; 1,1,1; 1,1,2

Crossrefs

Cf. A368030, A363203, A363204, A363207.
Showing 1-2 of 2 results.

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