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A253091
List of ternary words obtained by expanding (1+2x)^n mod 3 and reading the coefficients starting with the constant term.
2
1, 12, 111, 1002, 12021, 111222, 1001001, 12012012, 111111111, 1000000002, 12000000021, 111000000222, 1002000002001, 12021000021012, 111222000222111, 1001001002002002, 12012012021021021, 111111111222222222, 1000000001000000001, 12000000012000000012, 111000000111000000111
OFFSET
0,2
COMMENTS
Arises in the study of a cellular automaton whose cells are in one of three states: 0, 1, or 2.
EXAMPLE
The first few polynomials are:
1
1+2*x
1+x+x^2
1+2*x^3
1+2*x+2*x^3+x^4
1+x+x^2+2*x^3+2*x^4+2*x^5
1+x^3+x^6
1+2*x+x^3+2*x^4+x^6+2*x^7
1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8
1+2*x^9
1+2*x+2*x^9+x^10
1+x+x^2+2*x^9+2*x^10+2*x^11
1+2*x^3+2*x^9+x^12
...
MAPLE
M:=20;
F:=1+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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 13 2015
STATUS
approved