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A006996 a(n) = C(2n,n) mod 3.

%I A006996 M0021 #50 Jun 27 2025 01:02:55
%S A006996 1,2,0,2,1,0,0,0,0,2,1,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,2,1,0,1,2,0,0,
%T A006996 0,0,1,2,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A006996 0,0,0,0,0,0,0,0,0,0,0,0,0,2,1,0,1,2,0,0,0,0,1,2,0,2,1,0,0,0,0,0,0,0,0,0,0
%N A006996 a(n) = C(2n,n) mod 3.
%C A006996 Removing 0's from the sequence gives Thue-Morse sequence A001285 : 1,2,0,2,1,0,0,0,0,2,1,0,1,2,..->1,2,2,1,2,1,1,2,... - _Benoit Cloitre_, Jan 04 2004
%C A006996 a(n) = 0 if n in A074940, a(n) = 1 if n in A074939, a(n) = 2 if n in A074938.
%C A006996 Central terms of the triangle in A083093. - _Reinhard Zumkeller_, Jul 11 2013
%D A006996 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006996 Reinhard Zumkeller, <a href="/A006996/b006996.txt">Table of n, a(n) for n = 0..2187=3^7</a>
%H A006996 Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%H A006996 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%F A006996 a(n) = A000984(n) mod 3.
%F A006996 a(n) = A005704(n) mod 3. - _Benoit Cloitre_, Jan 04 2004
%F A006996 A fixed point of the morphism : 1 -> 120, 2 -> 210, 0 -> 000. - _Philippe Deléham_, Jan 08 2004
%t A006996 Table[ Mod[ Binomial[2n, n], 3], {n, 0, 104}] (* Or *)
%t A006996 Nest[ Function[ l, {Flatten[(l /. {0 -> {0, 0, 0}, 1 -> {1, 2, 0}, 2 -> {2, 1, 0}})]}], {1}, 7] (* _Robert G. Wilson v_, Mar 28 2005 *)
%o A006996 (Haskell)
%o A006996 a006996 n = a083093 (2 * n) n  -- _Reinhard Zumkeller_, Jul 11 2013
%o A006996 (PARI) a(n)=if(n==0, return(1)); if(vecmax(Set(digits(n,3)))>1, 0, 1 + n%2) \\ _Charles R Greathouse IV_, May 09 2016
%o A006996 (Python)
%o A006996 from gmpy2 import digits
%o A006996 def A006996(n): return 0 if '2' in digits(n,3) else 1+(n&1) # _Chai Wah Wu_, Jun 26 2025
%Y A006996 Cf. A001285.
%Y A006996 Cf. A074938, A074939, A074940.
%Y A006996 Cf. A083093.
%Y A006996 Cf. A000984, A005704.
%K A006996 nonn,easy
%O A006996 0,2
%A A006996 _N. J. A. Sloane_, _James Propp_