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Number of words of length n over an alphabet of size 4 that are not "bifix-free".
3

%I #8 Aug 19 2019 10:10:37

%S 0,0,4,16,76,304,1264,5056,20404,81616,327184,1308736,5237776,

%T 20951104,83815744,335262976,1341097036,5364388144,21457733104,

%U 85830932416,343324451056,1373297804224,5493194102464,21972776409856,87891117178864

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

%F Equals 4^n - A019309(n).

%F a(0)=a(1)=0, a(2n)=4^n + 4a(2n-1) - a(n), a(2n+1)=4a(2n). - _Emeric Deutsch_, Feb 04 2006

%p 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

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

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Jun 06 2004

%E More terms from _Emeric Deutsch_, Feb 04 2006