A127560 Number of fixed r-celled polyominoes with smallest containing rectangle measuring k by m, read in order r=A056556(n)+1, k=A056560(n)+1, m=A056558(n)+1.

1, 0, 1, 1, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 1, 0, 1, 8, 8, 1, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 1, 12, 25, 12, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 18, 44, 18, 0, 1, 16, 50, 50, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 32, 8, 0, 0, 38, 155, 155, 38, 0, 1, 20, 82, 120, 82, 20, 1

Offset: 0

Author

Graeme McRae, Jan 18 2007

Keywords

• nonn

Comments

The sum of each triangle, i.e. for a given r the sum of a(n) for all n such that r=A056556(n)+1 is the number of r-celled fixed polyominoes, A001168(r).

Examples

			The 5th triangle of the sequence, the number of fixed pentominoes by dimension, is
0,0,0,0,1
0,0,6,12
0,6,25
0,12
1
This indicates, for example, there are 25 fixed pentominos that fit in a 3 X 3 rectangle and 12 fixed pentominos that fit in a 4 X 2 rectangle.
		

Crossrefs

Cf. A000105, A000988, A001168 Indices for reading by triangles given by A056556, A056560, A056558.