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A143351 Expansion of x  / ( 1-x^2-x^4-x^7-x^8-x^9-x^10 ) 0
1, 0, 1, 0, 2, 0, 3, 1, 6, 3, 11, 7, 20, 15, 37, 32, 70, 68, 134, 141, 257, 288, 495, 583, 959, 1175, 1867, 2358, 3646, 4714, 7136, 9397, 13994, 18695, 27489, 37138, 54068, 73687, 106450, 146066, 209740, 289328, 413506, 572784, 815628, 1133455, 1609405 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A polynomial expansion sequence based on the Weaver telegraphic Polynomial: ( compare A122762): p(x)=-1 - x - x^2 - x^3 - x^6 - x^8 + x^10.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..47.

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

FORMULA

p(x)=Expand[x^10*Det[{{-1, (1/x^4 + 1/x^2)}, {(1/x^6 + 1/x^5), 1/x^2 + 1/x^4 - 1}}]]; p(x)=-1 - x - x^2 - x^3 - x^6 - x^8 + x^10; a(n)==coefficient_expansion(x^10*p(1/x)).

MATHEMATICA

f[x_] = -1 - x - x^2 - x^3 - x^6 - x^8 + x^10; g[x] = ExpandAll[x^10*f[1/x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]

CoefficientList[Series[x/(1-x^2-x^4-x^7-x^8-x^9-x^10), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 0, 1, 0, 0, 1, 1, 1, 1}, {0, 1, 0, 1, 0, 2, 0, 3, 1, 6}, 60] (* Harvey P. Dale, Mar 05 2016 *)

CROSSREFS

Cf. A122762.

Sequence in context: A130627 A006209 A005307 * A241644 A241640 A158449

Adjacent sequences:  A143348 A143349 A143350 * A143352 A143353 A143354

KEYWORD

nonn,uned

AUTHOR

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

EXTENSIONS

More terms from Harvey P. Dale, Mar 05 2016

STATUS

approved

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Last modified September 30 22:26 EDT 2020. Contains 337440 sequences. (Running on oeis4.)