A000104 Number of n-celled free polyominoes without holes. (Formerly M1424 N0560)

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

0,4

References

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).

Links

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.

Formula

a(n) = A000105(n) - A001419(n). - John Mason, Sep 06 2022

a(n) = (4*A056879(n) + 4*A056881(n) + 4*A056883(n) + 6*A056880(n) + 6*A056882(n) + 6*A357647(n) + 7*A357648(n) + A006724(n)) / 8. - John Mason, Oct 10 2022

Crossrefs

Cf. A000105, row sums of A308300, A006746, A056877, A006748, A056878, A006747, A006749, A054361, A070765 (polyiamonds), A018190 (polyhexes), A266549 (by perimeter).

Cf. A056879, A056880, A056881, A056882, A006724, A357647, A357648.

Sequence in context: A054359 A148287 A036357 * A342537 A000105 A055192

Adjacent sequences: A000101 A000102 A000103 * A000105 A000106 A000107

Keyword

nonn,nice,hard

Author

N. J. A. Sloane

Extensions

Extended to n=26 by Tomás Oliveira e Silva

a(27)-a(28) from Tomás Oliveira e Silva's page added by Andrey Zabolotskiy, Oct 02 2022

Status

approved