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A262616
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Triangle read by rows: T(n,k) = 4^(n-k), n>=0, 0<=k<=n.
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1
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1, 4, 1, 16, 4, 1, 64, 16, 4, 1, 256, 64, 16, 4, 1, 1024, 256, 64, 16, 4, 1, 4096, 1024, 256, 64, 16, 4, 1, 16384, 4096, 1024, 256, 64, 16, 4, 1, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1, 262144, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1, 1048576, 262144, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1
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OFFSET
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0,2
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COMMENTS
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A triangle of the same family of A130321 and A140303, with the same offset.
T(n,k) is also the number of hidden crosses of size k+1 formed by squares and rectangles in the toothpick structure of A139250 after 2^(n+2) stages. The last term in every row represents the central cross of the toothpick structure.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
4, 1;
16, 4, 1;
64, 16, 4, 1;
256, 64, 16, 4, 1;
1024, 256, 64, 16, 4, 1;
4096, 1024, 256, 64, 16, 4, 1;
16384, 4096, 1024, 256, 64, 16, 4, 1;
65536, 16384, 4096, 1024, 256, 64, 16, 4, 1;
262144, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1;
1048576, 262144, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1;
4194304, 1048576, 262144, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1;
...
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MATHEMATICA
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CROSSREFS
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Row sums give the positive terms of A002450.
Alternating row sums give the positive terms of A015521.
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KEYWORD
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AUTHOR
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STATUS
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approved
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