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A344110
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Triangle read by rows: T(n,k) = 2^(n*k), n >= 0, 0 <= k <= n.
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8
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1, 1, 2, 1, 4, 16, 1, 8, 64, 512, 1, 16, 256, 4096, 65536, 1, 32, 1024, 32768, 1048576, 33554432, 1, 64, 4096, 262144, 16777216, 1073741824, 68719476736, 1, 128, 16384, 2097152, 268435456, 34359738368, 4398046511104, 562949953421312
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OFFSET
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0,3
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COMMENTS
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T(n, k) is the number of relations from an n-element set into a k-element set, n >= 0, 0 <= k <= n.
T(n,k) is the size of the right principal ideal generated by A where A is an n X n matrix over GF(2) having rank k. The right principal ideal of A contains precisely the matrices whose image is contained in the image of A. - Geoffrey Critzer, Sep 25 2022
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LINKS
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FORMULA
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T(n,k) = 2^(n*k).
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EXAMPLE
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T(3,3) = number of relations from a 3-element set into a 3-element set=2^(3*3)=512.
Triangle begins:
1
1 2
1 4 16
1 8 64 512
1 16 256 4096 65536
1 32 1024 32768 1048576 33554432
...
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MATHEMATICA
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Table[2^(n*k), {n, 0, 10}, {k, 0, n}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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