OFFSET
1,3
COMMENTS
Here two polycubes that differ by reflection are considered different. - Joerg Arndt, Apr 26 2023
Number of oriented polyominoes with n cubical cells of the regular tiling with Schläfli symbol {4,3,4}. For oriented polyominoes, chiral pairs are counted as two. - Robert A. Russell, Mar 21 2024
REFERENCES
C. J. Bouwkamp, personal communication.
W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.
W. F. Lunnon, personal communication.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Nina Bohlmann and Ralf Benölken, Complex Tasks: Potentials and Pitfalls, Mathematics (2020) Vol. 8, No. 10, 1780.
C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971.
A. Clarke, Polycubes.
A. Clarke, The 8 tetracubes.
Stanley Dodds, C# program for this sequence.
Kevin L. Gong, Polyominoes Home Page.
M. Keller, Counting polyforms.
David A. Klarner, Some results concerning polyominoes, Fibonacci Quarterly 3 (1965), 9-20.
Jeffrey R. Long and R. H. Holm, Enumeration and structural classification of clusters derived from parent solids ..., J. Amer. Chem. Soc., 116 (1994), 9987-10002.
John Mason, Coordinate sets of examples of polycube symmetry
Phillip Thompson, Rust port of Stanley Dodds's algorithm.
Eric Weisstein's World of Mathematics, Polycube.
FORMULA
EXAMPLE
Table showing total number and numbers with each group order.
-------------------------------------------------------------
.n ...A000162 ..group:.1.....2...3...4.6.8.24
.1 .........1..........0.....0...0...0.0.0..1
.2 .........1..........0.....0...0...0.0.1..0
.3 .........2..........0.....1...0...0.0.1..0
.4 .........8..........1.....4...1...0.0.2..0
.5 ........29.........17....10...0...0.0.2..0
.6 .......166........127....34...0...3.1.1..0
.7 ......1023........941....71...4...5.0.1..1
.8 ......6922.......6662...246...0..11.0.2..1
.9 .....48311......47771...522...3..11.0.4..0
10 ....346543.....344708..1783..24..24.2.2..0
11 ...2522522....2518713..3765...4..35.0.5..0
12 ..18598427...18585455.12858..18..84.5.7..0
13 .138462649..138434899.27496.151..92.2.8..1
14 1039496297.1039401564.94525..25.174.4.5..0
CROSSREFS
KEYWORD
nonn,nice,hard,more
AUTHOR
EXTENSIONS
The old value for a(11), 2522572, was corrected by Achim Flammenkamp to 2522522, Feb 15 1999.
a(13)-a(14) from Brendan Owen (brendan_owen(AT)yahoo.com), Dec 27, 2001
a(15)-a(16) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007
a(17)-a(20) from Stanley Dodds, Dec 11 2023
a(21)-a(22) (using Dodds's algorithm) from Phillip Thompson, Feb 07 2024
STATUS
approved