A253091 List of ternary words obtained by expanding (1+2x)^n mod 3 and reading the coefficients starting with the constant term.

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.

Links

Table of n, a(n) for n=0..20.

Index entries for sequences related to cellular automata

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

Cf. A255285, A255286, A182069.

Sequence in context: A066042 A153597 A036733 * A123933 A199691 A348150

Adjacent sequences: A253088 A253089 A253090 * A253092 A253093 A253094

Keyword

nonn

Author

N. J. A. Sloane, Feb 13 2015

Status

approved