A006996 a(n) = C(2n,n) mod 3. (Formerly M0021)

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).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..2187=3^7

Michael Gilleland, Some Self-Similar Integer Sequences

Index entries for sequences that are fixed points of mappings

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
(Python)
from gmpy2 import digits
def A006996(n): return 0 if '2' in digits(n, 3) else 1+(n&1) # Chai Wah Wu, Jun 26 2025

Crossrefs

Cf. A001285.

Cf. A074938, A074939, A074940.

Cf. A083093.

Cf. A000984, A005704.

Sequence in context: A056615 A060989 A135298 * A321430 A343914 A386848

Adjacent sequences: A006993 A006994 A006995 * A006997 A006998 A006999

Keyword

nonn,easy

Author

N. J. A. Sloane, James Propp

Status

approved