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A228612
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Number of (possibly overlapping) occurrences of the subword given by the binary expansion of n in all binary words of length n.
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2
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0, 1, 1, 4, 4, 12, 32, 80, 80, 192, 448, 1024, 2304, 5120, 11264, 24576, 24576, 53248, 114688, 245760, 524288, 1114112, 2359296, 4980736, 10485760, 22020096, 46137344, 96468992, 201326592, 419430400, 872415232, 1811939328, 1811939328, 3758096384, 7784628224
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OFFSET
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0,4
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COMMENTS
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a(2^n) = a(2^n-1) for n>0.
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 4 because we have one subword 11 in each of 011, 110 and two overlapping occurrences of 11 in 111.
a(4) = 4 because we have one subword 100 in each of 0100, 1000, 1001, 1100 and no other occurrences in binary words of length 4.
a(5) = 12 because we have one subword 101 in each of 00101, 01010, 01011, 01101, 10100, 10110, 10111, 11010, 11011, 11101 and two overlapping occurrences of 101 in 10101.
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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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