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A360412
Number of binary words of length 2n with an even number of 1's which are not shuffle squares.
1
0, 0, 2, 10, 46, 192, 780, 3090, 12136, 47100, 181820, 697856, 2667642, 10157814, 38563342, 146002012, 551483230, 2078722874, 7821121318, 29378487188
OFFSET
0,3
COMMENTS
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.
FORMULA
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).
EXAMPLE
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.
CROSSREFS
Cf. A191755.
Sequence in context: A373913 A212387 A191813 * A181294 A080643 A032389
KEYWORD
nonn,more
AUTHOR
Bartlomiej Pawlik, Feb 07 2023
STATUS
approved