A006762 Number of strictly 2-dimensional fixed polyominoes with n cells. (Formerly M3534)

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

1,3

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.

Formula

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

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 *)

Crossrefs

A column of A195739.

Cf. A001168.

Sequence in context: A202974 A034331 A107278 * A297917 A202752 A286210

Adjacent sequences: A006759 A006760 A006761 * A006763 A006764 A006765

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved