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A006996
a(n) = C(2n,n) mod 3.
(Formerly M0021)
9
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, 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, 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
OFFSET
0,2
COMMENTS
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
a(n) = 0 if n in A074940, a(n) = 1 if n in A074939, a(n) = 2 if n in A074938.
Central terms of the triangle in A083093. - Reinhard Zumkeller, Jul 11 2013
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
FORMULA
a(n) = A000984(n) mod 3.
a(n)=A005704(n) mod 3. - Benoit Cloitre, Jan 04 2004
A fixed point of the morphism : 1 -> 120, 2 -> 210, 0 -> 000. - Philippe Deléham, Jan 08 2004
MATHEMATICA
Table[ Mod[ Binomial[2n, n], 3], {n, 0, 104}] (* Or *)
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 *)
PROG
(Haskell)
a006996 n = a083093 (2 * n) n -- Reinhard Zumkeller, Jul 11 2013
(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
CROSSREFS
Sequence in context: A056615 A060989 A135298 * A321430 A343914 A262774
KEYWORD
nonn,easy
STATUS
approved