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A255285
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List of ternary words obtained by expanding (2+x)^n mod 3 and reading the coefficients starting with the constant term.
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3
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1, 21, 111, 2001, 12021, 222111, 1001001, 21021021, 111111111, 2000000001, 12000000021, 222000000111, 1002000002001, 21012000012021, 111222000222111, 2002002001001001, 12012012021021021, 222222222111111111, 1000000001000000001, 21000000021000000021, 111000000111000000111
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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]
...
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MAPLE
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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:
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CROSSREFS
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For corresponding decimal numbers (set x=3 in these polynomials) see A182069.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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