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A337131
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Row lengths of irregular triangle A335967.
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2
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1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 2, 1, 2, 1, 1, 1, 1, 2, 1, 4, 8, 2, 2, 1, 1, 4, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 4, 1, 1, 4, 4, 16, 8, 2, 4, 2, 2, 1, 1, 2, 1, 4, 8, 2, 2, 1, 1, 4, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 4, 1, 1, 2, 2, 8, 4, 1, 2, 1, 1, 4, 4, 8, 4, 16, 32, 8
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listen;
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OFFSET
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1,5
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COMMENTS
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All terms are powers of 2.
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LINKS
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FORMULA
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a(2^k-1) = 1 for any k >= 0.
a(2^k) = 1 for any k >= 0.
a(A000975(k)) = 2^(k-2) for any k >= 2.
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EXAMPLE
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For n = 13, the binary representation of 13 is "1101", so we consider the tilings of a size 4 staircase polyomino whose base has the following shape:
.....
. .
. .....
. .
+---+ .....
| | .
| +---+---+---+
| 1 1 | 0 | 1 |
+-------+---+---+
There are two possible penultimate rows:
..... .....
. . . .
. ..... . .....
. | . . .
+---+ +---+ +---+---+---+
| 1 | 0 0 | | 1 | 0 | 1 |
| +---+---+---+ | +---+---+---+
| | | | | | | |
+-------+---+---+, +-------+---+---+
so a(13) = 2.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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