login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..106.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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