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A180444
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.
1
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, 34, 42, 28, 50, 30, 46, 44, 50, 44, 58, 36, 56, 52, 62, 40, 70, 42, 66, 64, 68, 46, 78, 54, 78, 68, 78, 52, 88, 68, 86, 76, 86, 58, 102, 60, 92, 88, 94, 80, 110, 66, 102, 92, 114, 70
OFFSET
0,2
LINKS
G. Fici, A Characterization of Bispecial Sturmian Words, MFCS 2012, Lecture Notes in Comput. Sci. 7464: 383-394 (2012)
FORMULA
a(n) = 2*(n+1) - phi(n+2).
MAPLE
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
MATHEMATICA
f[n_] := 2 n + 2 - EulerPhi[n + 2]; Array[f, 70, 0] (* Robert G. Wilson v, Sep 07 2010 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Fred Lunnon, Sep 05 2010
EXTENSIONS
More terms from Robert G. Wilson v, Sep 07 2010
STATUS
approved