|
Search: id:A142474
|
|
|
| A142474 |
|
Galois polynomial expansion ( called D transform in Booth) of GF(2^3): a(n)=expansion((1 + t)/(t^3 + t + 1)). |
|
+0
1
|
|
| 1, 0, 1, 2, 4, 9, 19, 41, 88, 189, 406, 872, 1873, 4023, 8641, 18560
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
The expansion of the GF(2) "binary" function is different than given in Booth: it is signed:
f(t)=(1+t)/(1+t+t^2);
The general function of this sort is for GF(2^n):
f(t,n)=(1+t)/(1+t+t^n).
|
|
REFERENCES
|
Taylor L. Booth, Sequential Machines and Automata Theory, John Wiley and Sons, Inc., 1967, page 331ff.
|
|
FORMULA
|
a(n)=expansion((1 + t)/(t^3 + t + 1)).
|
|
MATHEMATICA
|
Table[ ExpandAll[SeriesCoefficient[Series[(1 + t)/(t^3 + t + 1), {t, 0, 30}], n]], {n, 0, 30, 2}]
|
|
CROSSREFS
|
Sequence in context: A036616 A136298 A122584 this_sequence A141015 A141683 A078039
Adjacent sequences: A142471 A142472 A142473 this_sequence A142475 A142476 A142477
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 21 2008
|
|
|
Search completed in 0.002 seconds
|
