A094559 Number of words of length n over an alphabet of size 4 that are not "bifix-free".

0, 0, 4, 16, 76, 304, 1264, 5056, 20404, 81616, 327184, 1308736, 5237776, 20951104, 83815744, 335262976, 1341097036, 5364388144, 21457733104, 85830932416, 343324451056, 1373297804224, 5493194102464, 21972776409856, 87891117178864

Offset: 0

Author

N. J. A. Sloane, Jun 06 2004

Keywords

• nonn
• easy

Crossrefs

See A019308, A019309 and A003000 for much more information. Cf. A094578.

Programs

Maple

a:=proc(n) if n=0 or n=1 then 0 elif n mod 2 = 0 then 4*a(n-1)-a(n/2)+4^(n/2) else 4*a(n-1) fi end: seq(a(n),n=0..28); # Emeric Deutsch, Feb 04 2006

Formula

Equals 4^n - A019309(n).

a(0)=a(1)=0, a(2n)=4^n + 4a(2n-1) - a(n), a(2n+1)=4a(2n). - Emeric Deutsch, Feb 04 2006

Extensions

More terms from Emeric Deutsch, Feb 04 2006