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A360412
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Number of binary words of length 2n with an even number of 1's which are not shuffle squares.
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1
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0, 0, 2, 10, 46, 192, 780, 3090, 12136, 47100, 181820, 697856, 2667642, 10157814, 38563342, 146002012, 551483230, 2078722874, 7821121318, 29378487188
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OFFSET
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0,3
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COMMENTS
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A shuffle square is a word obtained by self-shuffling, e.g., the French word "tuteurer" is a shuffle square as it can be obtained by self-shuffling the word "tuer".
Words with an odd number of 1's obviously are not shuffle squares.
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LINKS
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FORMULA
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a(n) = 2^(2n-1) - A191755(n), since the number of binary words of length 2n with an even number of 1's is 2^(2n-1).
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EXAMPLE
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a(3)=10, since the binary words of length 6 with an even number of 1's which are not shuffle squares are 000110, 010001, 011000, 011101, 011110, 100001, 100010, 100111, 101110 and 111001.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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