A159782 a(0)=1; a(1)=a(2)=a(3)=a(4)=2; a(2n+1)=0 for n >= 2; a(4n)=a(4n-2) = a(n) + a(n+1) for n >= 2.

1, 2, 2, 2, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4

Offset: 0

Author

Philippe Deléham, Apr 22 2009

Keywords

• easy
• nonn

Comments

a(n) = {0, 1, 2 or 4}. - Robert G. Wilson v, May 27 2009

Also the number of palindromes of length n in the Thue-Morse sequence (A010060). - Jeffrey Shallit, Feb 19 2013

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• A. Blondin-Massé, S. Brlek, A. Garon, and S. Labbé, Combinatorial properties of f-palindromes in the Thue-Morse Sequence, Pure. Math. Appl., 19 (2-3) (2008), 39-52.

Crossrefs

Cf. A010060.

Programs

Mathematica

f[n_] := f[n]= Switch[ Mod[n, 4], 0, f[n/4] + f[n/4 + 1], 1, 0, 2, f[(n + 2)/4] + f[(n + 6)/4], 3, 0]; f[0] = 1; f[1] = f[2] = f[3] = f[4] = 2; Table[f@n, {n, 0, 104}] (* Robert G. Wilson v, May 27 2009 *)

Extensions

More terms from Robert G. Wilson v, May 27 2009