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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.
0

%I #4 Mar 30 2012 18:34:45

%S 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,

%T 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,

%U 0,0,0,0,8,32,8,0,0,38,155,155,38,0,1,20,82,120,82,20,1

%N 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.

%C 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).

%e The 5th triangle of the sequence, the number of fixed pentominoes by dimension, is

%e 0,0,0,0,1

%e 0,0,6,12

%e 0,6,25

%e 0,12

%e 1

%e 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.

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

%K nonn

%O 0,9

%A _Graeme McRae_, Jan 18 2007