A006762 Number of strictly 2-dimensional fixed polyominoes with n cells.

0, 0, 4, 17, 61, 214, 758, 2723, 9908, 36444, 135266, 505859, 1903888, 7204872, 27394664, 104592935, 400795842, 1540820540, 5940738674, 22964779658, 88983512781, 345532572676, 1344372335522, 5239988770266, 20457802016009, 79992676367106, 313224032098242, 1228088671826971

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This sequence counts only polyominoes that are strictly 2-dimensional - it excludes those where all the squares are in a single line. Thus for n > 1, a(n) = A001168(n) - 2. - Franklin T. Adams-Watters, Jul 29 2007

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..56
• W. F. Lunnon, Counting multidimensional polyominoes, Computer Journal 18 (1975), no. 4, pp. 366-367.

Crossrefs

A column of A195739.

Cf. A001168.

Programs

Mathematica

A001168 = Cases[Import["https://oeis.org/A001168/b001168.txt", "Table"], {, }][[All, 2]];
a[n_] := If[n == 1, 0, A001168[[n]] - 2];
Array[a, 56] (* Jean-François Alcover, Sep 06 2019 *)

Formula

a(n) = A001168(n) - 2 for n > 1. - Franklin T. Adams-Watters, Jul 29 2007

Extensions

Name clarified and a(18)-a(28) from Andrew Howroyd, Dec 04 2018