A226947 Number of runs of strictly increasing numbers of 2 X 2 squares in the list of partitions of an n X n square lattice into squares, considering only the list of parts, where partition sorting order is ascending with larger squares taking higher precedence.

1, 1, 2, 3, 4, 8, 12, 22, 45, 86, 155, 357, 675

Offset

1,3

Comments

The sequence was derived from the documents in the Links section. The documents are first specified in the Links section of A034295.

a(n) = row length of A226948(n).

Links

Table of n, a(n) for n=1..13.

Jon E. Schoenfield, Table of solutions for n <= 12

Alois P. Heinz, More ways to divide an 11 X 11 square into sub-squares

Alois P. Heinz, List of different ways to divide a 13 X 13 square into sub-squares

Example

For n = 3, the partitions are:
Square side 1 2 3
            9 0 0
            5 1 0
            0 0 1
So a(3) = 2 as there are 2 runs of 2 X 2 squares: (0,1) from the first 2 partitions and (0) from the third.

Crossrefs

Cf. A034295, A226948.

Sequence in context: A060200 A057608 A060984 * A272615 A356188 A238962

Adjacent sequences: A226944 A226945 A226946 * A226948 A226949 A226950

Keyword

nonn,more

Author

Christopher Hunt Gribble, Jun 23 2013

Status

approved