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EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 5*x^4 + 6*x^5 + 6*x^6 + 3*x^7 + 2*x^8 + 17*x^9 + 11*x^10 + 10*x^11 + 13*x^12 +...
The table of coefficients in A(x)^n reduced modulo 3 begins:
n=0: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
n=1: [1, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, ...];
n=2: [1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...];
n=3: [1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, ...];
n=4: [1, 1, 2, 0, 0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, ...];
n=5: [1, 2, 2, 0, 2, 2, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...];
n=6: [1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
n=7: [1, 1, 2, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, ...];
n=8: [1, 2, 2, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
n=9: [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, ...];
n=10:[1, 1, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, ...];
n=11:[1, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, ...];
n=12:[1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, ...];
n=13:[1, 1, 2, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 1, ...];
n=14:[1, 2, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 1, ...];
n=15:[1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, ...];
n=16:[1, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 1, ...];
n=17:[1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 2, 2, 1, 1, 1, 0, 0, 0, 1, ...];
n=18:[1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, ...];
n=19:[1, 1, 2, 2, 2, 0, 0, 0, 2, 1, 1, 2, 2, 2, 0, 0, 0, 1, 0, ...];
n=20:[1, 2, 2, 2, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0, 0, 0, 1, 1, 0, ...];
n=21:[1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, ...];
n=22:[1, 1, 2, 0, 0, 2, 1, 1, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 0, ...];
n=23:[1, 2, 2, 0, 2, 2, 1, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 0, 0, ...];
n=24:[1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, ...];
n=25:[1, 1, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, ...];
n=26:[1, 2, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0],...];
n=27:[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],...]; ...
where the antidiagonal sums form this sequence.
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