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%I #18 Apr 20 2014 03:11:35
%S 1,2,4,4,8,6,10,10,14,10,18,12,20,20,22,16,28,18,30,28,32,22,38,28,38,
%T 34,42,28,50,30,46,44,50,44,58,36,56,52,62,40,70,42,66,64,68,46,78,54,
%U 78,68,78,52,88,68,86,76,86,58,102,60,92,88,94,80,110,66,102,92,114,70
%N a(n) equals the number of bispecial Sturmian words of length n, that is words which are prefix to two words of length n+1, and likewise suffix. Note that prefix and suffix are not independent, unless the word is also palindromic: see A000010.
%H Vincenzo Librandi, <a href="/A180444/b180444.txt">Table of n, a(n) for n = 0..1000</a>
%H G. Fici, <a href="http://arxiv.org/abs/1204.1672">A Characterization of Bispecial Sturmian Words</a>, MFCS 2012, Lecture Notes in Comput. Sci. 7464: 383-394 (2012)
%F a(n) = 2*(n+1) - phi(n+2).
%p with(numtheory); A180444:=n->`if`(n=0, 1, 2*(n+1) - phi(n+2)); seq(A180444(n), n=0..50); # _Wesley Ivan Hurt_, Apr 19 2014
%t f[n_] := 2 n + 2 - EulerPhi[n + 2]; Array[f, 70, 0] (* _Robert G. Wilson v_, Sep 07 2010 *)
%Y Cf. A005598, A002088, A000010.
%K nonn
%O 0,2
%A _Fred Lunnon_, Sep 05 2010
%E More terms from _Robert G. Wilson v_, Sep 07 2010