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A142475
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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)).
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0
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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; internal format)
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OFFSET
| 1,23
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COMMENTS
| Row sums are:
{1, 0, -1, 0, 0, -2, 2, -3, 3, -7, 12, -20, 27, -37, 49}.
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REFERENCES
| Taylor L. Booth, Sequential Machines and Automata Theory, John Wiley and Sons, Inc., 1967, page 331ff.
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FORMULA
| p(x,n)=(1+x)/(x^n+x+1): t(n,m)=expansion(p(x,n)).
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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}
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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]
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CROSSREFS
| Cf. A078012.
Sequence in context: A015318 A026836 A089052 * A051556 A081602 A077267
Adjacent sequences: A142472 A142473 A142474 * A142476 A142477 A142478
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 21 2008
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