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A143389
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Coefficient Expansion sequence of a Weaver Morse Code polynomial: ( using Cylotomic prime base dot, dash, letter space and word space symbols) p(x)=-5 - 10 x - 12 x^2 - 10 x^3 - 7 x^4 - 3 x^5 + 5 x^7 + 8 x^8 + 9 x^9 + 8 x^10 + 6 x^11 + 3 x^12 + x^13.
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1, -3, 3, 1, -6, 7, -1, -9, 11, 7, -34, 32, 23, -95, 99, 27, -219, 250, 76, -571, 619, 241, -1517, 1684, 511, -3927, 4500, 1205, -10120, 11628, 3041
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, p37 - 38
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FORMULA
| p(x)=-5 - 10 x - 12 x^2 - 10 x^3 - 7 x^4 - 3 x^5 + 5 x^7 + 8 x^8 + 9 x^9 + 8 x^10 + 6 x^11 + 3 x^12 + x^13; a(n)=Coefficient_expansion(x^13*p(1/x)).
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EXAMPLE
| Weaver determinant:
A0 = Cyclotomic[2, x]
B0 = Cyclotomic[5, x]
C0 = Cyclotomic[3, x]
D0 = Cyclotomic[7, x]
Expand[FullSimplify[ExpandAll[((1 + x) (1 + x + x^2) (
1 + x + x^2 + x^3 + x^4) (
1 + x + x^2 + x^3 + x^4 + x^5 + x^6))*Det[{{-1, (1/B0 + 1/A0)}, {(1/
D0 + 1/C0),
1/A0 + 1/B0 - 1}}]]]]
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MAPLE
| p[x_] = -5 - 10 x - 12 x^2 - 10 x^3 - 7 x^4 - 3 x^5 + 5 x^7 + 8 x^8 + 9 x^9 + 8 x^10 + 6 x^11 + 3 x^12 + x^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
| Sequence in context: A010468 A082009 A110640 * A094040 A039798 A193560
Adjacent sequences: A143386 A143387 A143388 * A143390 A143391 A143392
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 22 2008
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