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
KEYWORD
nonn,more
AUTHOR
Bartlomiej Pawlik, Feb 07 2023
STATUS
approved