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Number of distinct sequences defined by the elements of powers >= 0 of n X n (0,1) matrices.

3

`%I #22 Apr 25 2014 19:49:42
`

`%S 2,13,132,3833,363288
`

`%N Number of distinct sequences defined by the elements of powers >= 0 of n X n (0,1) matrices.
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`%H Christopher Hunt Gribble, <a href="/A239748/a239748.cpp.txt">C++ Program</a>
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`%e a(2) = 13 because there are 13 distinct sequences in the set of 256 sequences formed by each element of each 2 X 2 binary matrix raised to successive powers >= 0. The first 10 terms of the distinct sequences and the frequencies of occurrence are:
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`%e Sequence Frequency
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`%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... 16
`

`%e 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ... 2
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`%e 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ... 2
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`%e 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 4
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`%e 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... 4
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`%e 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ... 2
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`%e 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, ... 2
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`%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... 12
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`%e 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ... 2
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`%e 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, ... 2
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`%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 12
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`%e 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... 2
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`%e 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, ... 2
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`%e . Total 64
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`%Y Cf. A238596.
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`%K nonn,hard,more
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`%O 1,1
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`%A _Christopher Hunt Gribble_, Mar 26 2014
`