cp's OEIS Frontend

A000104 Number of n-celled free polyominoes without holes.

%I A000104 M1424 N0560 #75 Mar 21 2024 21:03:41
%S A000104 1,1,1,2,5,12,35,107,363,1248,4460,16094,58937,217117,805475,3001127,
%T A000104 11230003,42161529,158781106,599563893,2269506062,8609442688,
%U A000104 32725637373,124621833354,475368834568,1816103345752,6948228104703,26618671505989,102102788362303
%N A000104 Number of n-celled free polyominoes without holes.
%D A000104 J. S. Madachy, Pentominoes - Some Solved and Unsolved Problems, J. Rec. Math., 2 (1969), 181-188.
%D A000104 George E. Martin, Polyominoes - A Guide to Puzzles and Problems in Tiling, The Mathematical Association of America, 1996
%D A000104 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000104 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000104 John Mason, <a href="/A000104/b000104.txt">Table of n, a(n) for n = 0..40</a>
%H A000104 Elena V. Konstantinova and Maxim V. Vidyuk, <a href="http://dx.doi.org/10.1021/ci025659y">Discriminating tests of information and topological indices. Animals and trees</a>, J. Chem. Inf. Comput. Sci. 43 (2003), 1860-1871.
%H A000104 John Mason, <a href="/A000104/a000104_2.pdf">Description of counting programs</a>
%H A000104 John Mason, <a href="/A000104/a000104.txt">Programs for calculation of numbers of unholey polyominoes</a>
%H A000104 Lucia Moura and Ivan Stojmenovic, <a href="https://doi.org/10.1002/9780470175668.ch2">Backtracking and Isomorph-Free Generation of Polyhexes</a>, Table 2.2 on p. 55 of Handbook of Applied Algorithms (2008).
%H A000104 W. R. Muller, K. Szymanski, J. V. Knop, and N. Trinajstic, <a href="https://doi.org/10.1007/BF01130823">On the number of square-cell configurations</a>, Theor. Chim. Acta 86 (1993) 269-278
%H A000104 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/animals.html">Enumeration of polyominoes</a>
%H A000104 T. R. Parkin, L. J. Lander, and D. R. Parkin, <a href="/A000104/a000104.pdf">Polyomino Enumeration Results</a>, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy)
%H A000104 R. C. Read, <a href="http://dx.doi.org/10.4153/CJM-1962-001-2">Contributions to the cell growth problem</a>, Canad. J. Math., 14 (1962), 1-20.
%F A000104 a(n) = A000105(n) - A001419(n). - _John Mason_, Sep 06 2022
%F A000104 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
%Y A000104 Cf. A000105, row sums of A308300, A006746, A056877, A006748, A056878, A006747, A006749, A054361, A070765 (polyiamonds), A018190 (polyhexes), A266549 (by perimeter).
%Y A000104 Cf. A056879, A056880, A056881, A056882, A006724, A357647, A357648.
%K A000104 nonn,nice,hard
%O A000104 0,4
%A A000104 _N. J. A. Sloane_
%E A000104 Extended to n=26 by Tomás Oliveira e Silva
%E A000104 a(27)-a(28) from Tomás Oliveira e Silva's page added by _Andrey Zabolotskiy_, Oct 02 2022