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Search: id:A143373
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| A143373 |
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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. |
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+0
1
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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An alternative set of symbols would be:
dot:x;
dash:x^2;
Letter space: x^3 ;
Word space: x^4 ;
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REFERENCES
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Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, p37 - 38
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FORMULA
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p(y)=-1 - 2 y^2 - 2 y^4 - y^6 + y^7; a(n)=coefficient_expansion(x^13*p(1/x))
G.f.: -x/(-1+x+2*x^3+2*x^5+x^7) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]
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EXAMPLE
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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}}]]]].
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A122762.
Sequence in context: A018162 A077879 A078140 this_sequence A102475 A066173 A114322
Adjacent sequences: A143370 A143371 A143372 this_sequence A143374 A143375 A143376
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 22 2008
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EXTENSIONS
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G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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