login
A255285
List of ternary words obtained by expanding (2+x)^n mod 3 and reading the coefficients starting with the constant term.
3
1, 21, 111, 2001, 12021, 222111, 1001001, 21021021, 111111111, 2000000001, 12000000021, 222000000111, 1002000002001, 21012000012021, 111222000222111, 2002002001001001, 12012012021021021, 222222222111111111, 1000000001000000001, 21000000021000000021, 111000000111000000111
OFFSET
0,2
COMMENTS
Alternatively, list of ternary words obtained by expanding (1+2x)^n mod 3 and reading the coefficients starting with the highest order term.
Arises in the study of a cellular automaton whose cells are in one of three states: 0, 1, or 2.
EXAMPLE
The coefficient lists of the first few polynomials are:
[1]
[2, 1]
[1, 1, 1]
[2, 0, 0, 1]
[1, 2, 0, 2, 1]
[2, 2, 2, 1, 1, 1]
[1, 0, 0, 1, 0, 0, 1]
[2, 1, 0, 2, 1, 0, 2, 1]
[1, 1, 1, 1, 1, 1, 1, 1, 1]
[2, 0, 0, 0, 0, 0, 0, 0, 0, 1]
...
MAPLE
M:=20;
F:=2+x mod 3;
g:=n->expand(F^n) mod 3;
g2:=n->series(g(n), x, M+6);
for n from 0 to M do lprint(seriestolist(g2(n))); od:
CROSSREFS
Mirror image of A253091.
For corresponding decimal numbers (set x=3 in these polynomials) see A182069.
Sequence in context: A039456 A182827 A364268 * A157265 A275916 A355510
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 21 2015
STATUS
approved