A360412 Number of binary words of length 2n with an even number of 1's which are not shuffle squares.

0, 0, 2, 10, 46, 192, 780, 3090, 12136, 47100, 181820, 697856, 2667642, 10157814, 38563342, 146002012, 551483230, 2078722874, 7821121318, 29378487188

Offset: 0

Author

Bartlomiej Pawlik, Feb 07 2023

Keywords

• nonn
• more

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.

Examples

			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.

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).