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A227998
Number T(n,k,s) of partitions of an n X k rectangle into s integer-sided squares, considering only the list of parts; irregular triangle T(n,k,s), 1 <= k <= n, s >= 1, read by rows.
3
1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0
OFFSET
1
The number of entries per row is n*k.
Christopher Hunt Gribble, C++ program
FORMULA
T(n,n,s) = A226912(n,s).
Sum_{s=1..n*k} T(n,k,s) = A224697(n,k), 1 <= k <= n.
EXAMPLE
T(6,4,6) = 2 because there are 2 partitions of a 6 X 4 rectangle into integer-sided squares with exactly 6 parts:
(6 2 X 2 squares) and
(4 1 X 1 squares, 1 2 X 2 square, 1 4 X 4 square).
The irregular triangle starts:
n,k Number of Square Parts s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ...
1,1 1
2,1 0 1
2,2 1 0 0 1
3,1 0 0 1
3,2 0 0 1 0 0 1
3,3 1 0 0 0 0 1 0 0 1
4,1 0 0 0 1
4,2 0 1 0 0 1 0 0 1
4,3 0 0 0 1 0 1 0 0 1 0 0 1
4,4 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1
5,1 0 0 0 0 1
5,2 0 0 0 1 0 0 1 0 0 1
5,3 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1
5,4 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 ...
5,5 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 ...
6,1 0 0 0 0 0 1
6,2 0 0 1 0 0 1 0 0 1 0 0 1
6,3 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1
6,4 0 0 1 0 0 2 0 1 2 1 0 1 1 0 1 1 0 1 ...
6,5 0 0 0 1 1 0 1 1 1 1 2 1 1 2 1 0 1 1 ...
6,6 1 0 0 1 0 1 0 0 3 0 1 4 1 1 2 1 1 2 ...
CROSSREFS
Sequence in context: A280816 A265246 A138709 * A266514 A082960 A320815
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved

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Last modified September 20 09:27 EDT 2024. Contains 376068 sequences. (Running on oeis4.)