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A228107
Triangle read by rows: T(n,k) (1 <= k <= n) = number of runs of strictly increasing numbers of 2 X 2 squares in the list of partitions of an n X k rectangle into integer-sided squares, considering only the list of parts, where partition sorting order is ascending with larger squares taking higher precedence.
2
1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 4, 1, 1, 3, 4, 5, 8, 1, 1, 3, 5, 6, 10, 12, 1, 1, 3, 6, 8, 13, 17, 22
OFFSET
1,6
LINKS
Christopher Hunt Gribble, C++ program
EXAMPLE
The triangle begins:
\ k 1 2 3 4 5 6 7 8 ...
n
1 1
2 1 1
3 1 1 2
4 1 1 2 3
5 1 1 2 3 4
6 1 1 3 4 5 8
7 1 1 3 5 6 10 12
8 1 1 3 6 8 13 17 22
...
T(5,4) = 3 because there are 3 runs of strictly increasing numbers of 2 X 2 squares in the list of partitions of a 5 X 4 rectangle into integer-sided squares. The list of partitions is:
. Square side
Run 1 2 3 4
. 1 20 0 0 0
. 16 1 0 0
. 12 2 0 0
. 8 3 0 0
. 4 4 0 0
. 2 11 0 1 0
. 7 1 1 0
. 3 2 1 0
. 3 4 0 0 1
CROSSREFS
Diagonal is A226947.
Sequence in context: A128227 A306727 A324209 * A140207 A104763 A027751
KEYWORD
nonn,tabl,more
AUTHOR
STATUS
approved