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 A142475 The D transform expansions of Galois GF(2^n) polynomials: p(x,n)=(1+x)/(x^n+x+1): t(n,m)=expansion(p(x,n)). 0
 1, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, -1, -1, 1, -1, 0, 0, 1, 2, -1, 1, -1, 0, 0, 0, -3, 1, -1, 1, -1, 0, 0, -1, 4, 0, 1, -1, 1, -1, 0, 0, 1, -6, -1, -1, 1, -1, 1, -1, 0, 0, 0, 9, 2, 2, -1, 1, -1, 1, -1, 0, 0, -1, -13, -3, -3, 1, -1, 1, -1, 1, -1, 0, 0, 1, 19, 3, 4, 0, 1, -1, 1, -1, 1, -1, 0, 0, 0, -28, -2, -5, -1, -1, 1, -1, 1, -1, 1, -1, 0, 0, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,23 COMMENTS Row sums are: {1, 0, -1, 0, 0, -2, 2, -3, 3, -7, 12, -20, 27, -37, 49}. REFERENCES Taylor L. Booth, Sequential Machines and Automata Theory, John Wiley and Sons, Inc., 1967, page 331ff. LINKS FORMULA p(x,n)=(1+x)/(x^n+x+1): t(n,m)=expansion(p(x,n)). EXAMPLE {1}, {0, 0}, {-1, 0, 0}, {1, -1, 0, 0}, {0, 1, -1, 0, 0}, {-1, -1, 1, -1, 0, 0}, {1, 2, -1, 1, -1, 0, 0}, {0, -3, 1, -1, 1, -1, 0, 0}, {-1, 4, 0, 1, -1, 1, -1, 0, 0}, {1, -6, -1, -1, 1, -1, 1, -1, 0, 0}, {0, 9, 2, 2, -1, 1, -1, 1, -1,0, 0}, {-1, -13, -3, -3, 1, -1, 1, -1, 1, -1, 0, 0}, {1, 19, 3,4, 0, 1, -1, 1, -1, 1, -1, 0, 0}, {0, -28, -2, -5, -1, -1, 1, -1, 1, -1, 1, -1, 0, 0}, {-1, 41, 0, 6, 2, 2, -1, 1, -1, 1, -1, 1, -1, 0, 0} MATHEMATICA a = Table[Table[ ExpandAll[SeriesCoefficient[Series[(1 + t)/(t^m + t + 1), {t, 0, 30}], n]], {n, 0, 30}], {m, 2, 32}]; b = Table[Table[a[[n]][[m]], {n, 1, m }], {m, 1, 15}] ; Flatten[b] CROSSREFS Cf. A078012. Sequence in context: A284606 A284019 A286135 * A051556 A330166 A081602 Adjacent sequences:  A142472 A142473 A142474 * A142476 A142477 A142478 KEYWORD uned,sign AUTHOR Roger L. Bagula, Sep 21 2008 STATUS approved

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Last modified August 8 18:36 EDT 2020. Contains 336298 sequences. (Running on oeis4.)