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A143373 Expansion of x / (1-x-2*x^3-2*x^5-x^7). 1
1, 1, 1, 3, 5, 9, 17, 30, 55, 100, 181, 330, 599, 1088, 1978, 3593, 6529, 11864, 21556, 39169, 71171, 129319, 234978, 426961, 775801, 1409655, 2561384, 4654113, 8456664, 15366012, 27920509 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A new 4 symbol polynomial of the Weaver telegraphic type ( simplified) : dot:x; dash:x^3; Letter space: x^2 ; Word space: x^4 ; p(y)=-1 - 2 y^2 - 2 y^4 - y^6 + y^7.

An alternative set of symbols would be:

dot:x;

dash:x^2;

Letter space: x^3 ;

Word space: x^4 ;

REFERENCES

Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, p37 - 38

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,2,0,2,0,1).

EXAMPLE

Weaver determinant:

Expand[FullSimplify[ExpandAll[y^7 *Det[{{-1, (1/y^3 + 1/y)}, {(1/y^4 + 1/y^2),1/y + 1/y^3 - 1}}]]]].

MATHEMATICA

p[y_] = -1 - 2 y^2 - 2 y^4 - y^6 + y^7; q[x_] = ExpandAll[x^13*p[1/x]]; a = Table[SeriesCoefficient[Series[1/q[x], {x, 0, 30}], n], {n, 0, 30}]

PROG

(PARI) x='x+O('x^50); Vec(x/(1-x-2*x^3-2*x^5-x^7)) \\ G. C. Greubel, Sep 27 2017

CROSSREFS

Cf. A122762.

Sequence in context: A288233 A288232 A289261 * A282184 A102475 A066173

Adjacent sequences:  A143370 A143371 A143372 * A143374 A143375 A143376

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 22 2008

STATUS

approved

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Last modified September 25 20:53 EDT 2018. Contains 315425 sequences. (Running on oeis4.)