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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

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

LINKS

Table of n, a(n) for n=1..36.

Christopher Hunt Gribble, C++ program

EXAMPLE

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.

Cf. A228106

Sequence in context: A176484 A144328 A128227 * A140207 A104763 A027751

Adjacent sequences:  A228104 A228105 A228106 * A228108 A228109 A228110

KEYWORD

nonn,tabl

AUTHOR

Christopher Hunt Gribble, Aug 10 2013

STATUS

approved

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Last modified December 15 08:50 EST 2018. Contains 318148 sequences. (Running on oeis4.)