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A360629
Triangle read by rows: T(n,k) is the number of sets of integer-sided rectangular pieces that can tile an n X k rectangle, 1 <= k <= n.
10
1, 2, 4, 3, 10, 21, 5, 22, 73, 192, 7, 44, 190, 703, 2035, 11, 91, 510, 2287, 8581, 27407, 15, 172, 1196, 6738, 30209, 118461
OFFSET
1,2
COMMENTS
Pieces are free to rotate by 90 degrees, i.e., an r X s piece and an s X r piece are equivalent. See A360451 for the case when the pieces are fixed.
EXAMPLE
Triangle begins:
n\k| 1 2 3 4 5 6 7
---+---------------------------------
1 | 1
2 | 2 4
3 | 3 10 21
4 | 5 22 73 192
5 | 7 44 190 703 2035
6 | 11 91 510 2287 8581 27407
7 | 15 172 1196 6738 30209 118461 ?
T(2,2) = 4, because a 2 X 2 rectangle can be tiled by: one 2 X 2 piece; two 1 X 2 pieces; one 1 X 2 piece and two 1 X 1 pieces; four 1 X 1 pieces.
The T(3,2) = 10 sets of pieces that can tile a 3 X 2 rectangle are shown in the table below. (Each column on the right gives a set of pieces.)
length X width | number of pieces
---------------+--------------------
2 X 3 | 1 0 0 0 0 0 0 0 0 0
2 X 2 | 0 1 1 0 0 0 0 0 0 0
1 X 3 | 0 0 0 2 1 1 0 0 0 0
1 X 2 | 0 1 0 0 1 0 3 2 1 0
1 X 1 | 0 0 2 0 1 3 0 2 4 6
CROSSREFS
Cf. A000041 (column k=1), A116694, A224697 (square pieces), A360451 (fixed pieces), A360630 (main diagonal), A360631 (column k=2), A360632 (column k=3).
Sequence in context: A270600 A350231 A349575 * A180871 A305423 A271866
KEYWORD
nonn,tabl,more
AUTHOR
STATUS
approved