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A361001
Triangle read by rows: T(n,k) is the number of tilings of an n X k rectangle by integer-sided rectangular pieces that cannot be rearranged to produce a different tiling of the rectangle (except rotations and reflections of the original tiling), 1 <= k <= n.
5
1, 2, 4, 3, 7, 9, 4, 11, 18, 23, 4, 14, 22, 34, 41, 6, 23, 42, 72, 108
OFFSET
1,2
FORMULA
T(n,1) = A361003(n) = A000005(n) + floor((n-1)/2). (The first term corresponds to cases where all pieces have the same size, the second to cases where there are two pieces of different sizes.)
EXAMPLE
Triangle begins:
n\k| 1 2 3 4 5 6
---+-------------------
1 | 1
2 | 2 4
3 | 3 7 9
4 | 4 11 18 23
5 | 4 14 22 34 41
6 | 6 23 42 72 108 ?
The T(3,3) = 9 nonrearrangeable tilings of the 3 X 3 square are:
+---+---+---+ +---+---+---+ +---+---+---+
| | | | | | |
+ + +---+---+---+ +---+---+---+
| | | | | |
+ + + + + +
| | | | | |
+---+---+---+ +---+---+---+ +---+---+---+
.
+---+---+---+ +---+---+---+ +---+---+---+
| | | | | | | | | | |
+---+---+---+ +---+---+ + +---+---+ +
| | | | | | | |
+ + + + + + + +
| | | | | | | |
+---+---+---+ +---+---+---+ +---+---+---+
.
+---+---+---+ +---+---+---+ +---+---+---+
| | | | | | | | | |
+---+---+---+ +---+---+---+ +---+---+---+
| | | | | | | | |
+ +---+ +---+---+---+ +---+---+---+
| | | | | | | | |
+---+---+---+ +---+---+---+ +---+---+---+
CROSSREFS
Cf. A000005, A360629, A360998, A361002 (main diagonal), A361003 (first column), A361004 (second column), A361005 (third column).
Sequence in context: A127002 A027634 A355564 * A223838 A224146 A225010
KEYWORD
nonn,tabl,more
AUTHOR
STATUS
approved