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A143375
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Expansion of x / ( 1 -x^2 -2*x^5 -x^8 -x^10 -x^12 ).
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0
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1, 0, 1, 0, 1, 2, 1, 4, 2, 6, 8, 8, 19, 14, 34, 36, 54, 86, 93, 172, 194, 308, 427, 552, 878, 1076, 1675, 2224, 3120, 4546, 5986
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| A new 4 symbol polynomial of the Weaver telegraphic type ( Prime like powers) : dot:x^2; dash:x^5; Letter space: x^3 ; Word space: x^7 ; p(x)=-1 - x^2 - x^4 - 2 x^7 - x^10 + x^12.
At C=-Log[0.7139184783743413]=0.336986 this has a lower channel capacity
than the Weaver C=0.539.
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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
| a(n) = +a(n-2) +2*a(n-5) +a(n-8) +a(n-10) +a(n-12).
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EXAMPLE
| Weaver determinant:
A0 = x^2;
B0 = x^5;
C0 = x^3;
D0 = x^7;
Expand[FullSimplify[ExpandAll[x^12*Det[{{-1, (1/B0 + 1/A0)}, {(1/D0 + 1/C0),
1/A0 + 1/B0 - 1}}]]]]
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MATHEMATICA
| p[x_] = -1 - x^2 - x^4 - 2 x^7 - x^10 + x^12; q[x_] = ExpandAll[x^12*p[1/x]]; a = Table[SeriesCoefficient[Series[1/q[x], {x, 0, 30}], n], {n, 0, 30}]
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CROSSREFS
| Cf. A122762.
Sequence in context: A176837 A007690 A205685 * A074364 A008796 A079966
Adjacent sequences: A143372 A143373 A143374 * A143376 A143377 A143378
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 22 2008
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