A000104
Number of n-celled free polyominoes without holes.
Original entry on oeis.org
1, 1, 1, 2, 5, 12, 35, 107, 363, 1248, 4460, 16094, 58937, 217117, 805475, 3001127, 11230003, 42161529, 158781106, 599563893, 2269506062, 8609442688, 32725637373, 124621833354, 475368834568, 1816103345752, 6948228104703, 26618671505989, 102102788362303
Offset: 0
- J. S. Madachy, Pentominoes - Some Solved and Unsolved Problems, J. Rec. Math., 2 (1969), 181-188.
- George E. Martin, Polyominoes - A Guide to Puzzles and Problems in Tiling, The Mathematical Association of America, 1996
- 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).
- John Mason, Table of n, a(n) for n = 0..40
- Elena V. Konstantinova and Maxim V. Vidyuk, Discriminating tests of information and topological indices. Animals and trees, J. Chem. Inf. Comput. Sci. 43 (2003), 1860-1871.
- John Mason, Description of counting programs
- John Mason, Programs for calculation of numbers of unholey polyominoes
- Lucia Moura and Ivan Stojmenovic, Backtracking and Isomorph-Free Generation of Polyhexes, Table 2.2 on p. 55 of Handbook of Applied Algorithms (2008).
- W. R. Muller, K. Szymanski, J. V. Knop, and N. Trinajstic, On the number of square-cell configurations, Theor. Chim. Acta 86 (1993) 269-278
- Tomás Oliveira e Silva, Enumeration of polyominoes
- T. R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy)
- R. C. Read, Contributions to the cell growth problem, Canad. J. Math., 14 (1962), 1-20.
Cf.
A000105, row sums of
A308300,
A006746,
A056877,
A006748,
A056878,
A006747,
A006749,
A054361,
A070765 (polyiamonds),
A018190 (polyhexes),
A266549 (by perimeter).
Extended to n=26 by Tomás Oliveira e Silva
A057409
Number of self-avoiding polygons of area n with any number of (self-avoiding polygon) holes on square lattice (not allowing rotations).
Original entry on oeis.org
1, 2, 6, 19, 63, 216, 756, 2685, 9650, 35018, 128084, 471623, 1746492, 6499356, 24290272, 91123171, 342984175, 1294829776, 4901319978, 18597856445, 70723784744, 269486503694, 1028736811230, 3933715966653
Offset: 1
A259857
Triangle T(n,k), n>=1, 2<=k<=n+1, read by rows, where T(n,k) is the number of self-avoiding square-lattice polygons by area n and perimeter 2*k.
Original entry on oeis.org
1, 0, 2, 0, 0, 6, 0, 0, 1, 18, 0, 0, 0, 8, 55, 0, 0, 0, 2, 40, 174, 0, 0, 0, 0, 22, 168, 566, 0, 0, 0, 0, 6, 134, 676, 1868, 0, 0, 0, 0, 1, 72, 656, 2672, 6237, 0, 0, 0, 0, 0, 30, 482, 2992, 10376, 21050, 0, 0, 0, 0, 0, 8, 310, 2592, 13160, 39824, 71666, 0, 0, 0, 0, 0, 2, 151, 2086, 12862, 56162, 151878, 245696
Offset: 1
Triangle begins:
==========================================================
n\k | 2 3 4 5 6 7 8 9 10 11 12 13
-----|----------------------------------------------------
1 | 1,
2 | 0,2,
3 | 0,0,6,
4 | 0,0,1,18
5 | 0,0,0, 8,55,
6 | 0,0,0, 2,40,174,
7 | 0,0,0, 0,22,168,566,
8 | 0,0,0, 0, 6,134,676,1868,
9 | 0,0,0, 0, 1, 72,656,2672, 6237,
10 | 0,0,0, 0, 0, 30,482,2992,10376,21050,
11 | 0,0,0, 0, 0, 8,310,2592,13160,39824, 71666,
12 | 0,0,0, 0, 0, 2,151,2086,12862,56162,151878,245696,
A341630
Number of fixed polyiamonds of area n without holes.
Original entry on oeis.org
2, 3, 6, 14, 36, 94, 250, 675, 1832, 5005, 13746, 37901, 104902, 291312, 811346, 2265905, 6343854, 17801383, 50057400, 141034248, 398070362, 1125426581, 3186725646, 9036406687, 25658313188, 72946289247, 207628101578, 591622990214, 1687527542874, 4818113792640
Offset: 1
Cf.
A001420 (polyiamonds with holes allowed; first deviates at n=9),
A036418 (polyiamonds with given perimeter, i.e. paths with given length),
A070765 (free polyiamonds, i.e. reduced for symmetry: rotations and reflections are allowed),
A006724 (analog for square lattice).
Showing 1-4 of 4 results.
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