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, 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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Cf. A005598, A002088, A000010.

Sequence in context: A079890 A337973 A223592 * A065608 A184396 A329718

Adjacent sequences: A180441 A180442 A180443 * A180445 A180446 A180447

Keyword

nonn

Author

Fred Lunnon, Sep 05 2010

Extensions

More terms from Robert G. Wilson v, Sep 07 2010

Status

approved