|
Search: id:A142475
|
|
|
| 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
|
|
| 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; listen)
|
|
|
OFFSET
|
1,23
|
|
|
COMMENT
|
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.
|
|
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: A015318 A026836 A089052 this_sequence A051556 A081602 A077267
Adjacent sequences: A142472 A142473 A142474 this_sequence A142476 A142477 A142478
|
|
KEYWORD
|
uned,sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 21 2008
|
|
|
Search completed in 0.002 seconds
|
