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A226948
Irregular triangle: T(n,k) is the number of partitions in each run 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. The sorting order for the list of partitions is ascending with larger squares taking higher precedence.
3
1, 2, 2, 1, 5, 1, 1, 5, 4, 1, 1, 10, 6, 4, 2, 1, 6, 1, 1, 10, 9, 8, 5, 1, 6, 5, 4, 1, 6, 1, 1, 17, 13, 11, 9, 8, 13, 9, 7, 5, 9, 5, 3, 5, 1, 1, 8, 6, 5, 3, 8, 1, 1, 17, 16, 15, 14, 11, 10, 6, 4, 2, 1, 13, 12, 11, 10, 7, 6, 9, 8, 7, 5, 5, 4, 1, 13, 12, 9, 7, 3, 1, 9, 8, 5, 3, 5, 4, 1, 8, 7, 6, 4, 2, 1, 8, 1, 1
OFFSET
1,2
COMMENTS
The sequence was derived from the documents in the Links section. The documents are first specified in the Links section of A034295.
The n-th row of the irregular triangle contains A226947(n) elements.
FORMULA
T(n,1) = A002522(floor(n/2)).
EXAMPLE
For n = 3, the partitions are:
Square side 1 2 3
9 0 0
5 1 0
0 0 1
So T(3,1) = 2, the length of the run of 2 X 2 squares (0,1) from the first 2 partitions and T(3,2) = 1, the length of the run of 2 X 2 squares (0) from the third. The irregular triangle begins:
\ k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ...
n
01 1
02 2
03 2 1
04 5 1 1
05 5 4 1 1
06 10 6 4 2 1 6 1 1
07 10 9 8 5 1 6 5 4 1 6 1 1
08 17 13 11 9 8 13 9 7 5 9 5 3 5 1 1 8 6 5 ...
09 17 16 15 14 11 10 6 4 2 1 13 12 11 10 7 6 9 8 ...
10 26 22 20 18 17 13 12 9 5 1 22 18 16 14 13 9 8 5 ...
11 26 25 24 23 21 19 17 14 13 10 22 21 20 19 17 15 13 10 ...
12 37 33 31 29 28 24 23 20 19 15 14 11 10 6 4 2 1 33 ...
13 37 36 35 34 33 31 29 26 25 22 20 17 15 13 9 5 1 33 ...
CROSSREFS
Row sums give: A034295.
Cf. A226947.
Sequence in context: A350825 A218529 A192456 * A010243 A332963 A203953
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved