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Search: id:A143372
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| A143372 |
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A new 4 symbol polynomial of the Weaver telegraphic type: dot:x^2; dash:x^4; Letter space:2 + x^2 + x^3; Word space:1 + x- x^3 - x^4 + x^6; p(y)=-5 - 3 y - 7 y^2 - 3 y^3 + 2 y^4 + 3 y^5 + 2 y^6 + 2 y^7 - 3 y^8 - y^9 - y^10 - 2 y^11 + y^12 + y^13. |
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+0
1
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| 1, -1, 3, -4, 10, -13, 27, -38, 70, -99, 173, -242, 400, -548, 869, -1136, 1718, -2088, 2936, -3033, 3615, -1763, -513, 10082, -24172, 58958, -111749, 220258, -385285, 693194, -1157154
(list; graph; listen)
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OFFSET
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1,3
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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)=-5 - 3 y - 7 y^2 - 3 y^3 + 2 y^4 + 3 y^5 + 2 y^6 + 2 y^7 - 3 y^8 - y^9 - y^10 - 2 y^11 + y^12 + y^13; a(n)=coefficient_expansion(x^13*p(1/x))
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EXAMPLE
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Weaver determinant:
Expand[FullSimplify[ExpandAll[y^4 *(2 + y^2 + y^3)(1 +y - y^3 - y^4 + y^6)*Det[{{-1, ((1/y^4 + 1/y^2))},
{1/((1 + y - y^3 - y^4 +y^6)) + 1/((2 + y^2 + y^3), 1/y^2 + 1/y^4 - 1}}]]]].
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MATHEMATICA
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p[y_] = -5 - 3 y - 7 y^2 - 3 y^3 + 2 y^4 + 3 y^5 + 2 y^6 + 2 y^7 - 3 y^8 - y^9 - y^10 - 2 y^11 + y^12 + y^13; 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: A031367 A073443 A092119 this_sequence A035594 A167273 A096380
Adjacent sequences: A143369 A143370 A143371 this_sequence A143373 A143374 A143375
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KEYWORD
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uned,probation,sign
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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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