Search: id:A143375
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%I A143375
%S A143375 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,
%T A143375 1076,1675,2224,3120,4546,5986
%N A143375 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.
%C A143375 At C=-Log[0.7139184783743413]=0.336986 this has a lower channel capacity
%C A143375 than the Weaver C=0.539.
%D A143375 Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, 
               University of Illinois Press, Chicago, 1963, p37 - 38
%F A143375 p(x)=-1 - x^2 - x^4 - 2 x^7 - x^10 + x^12; a(n)=coefficient_expansion(x^13*p(1/
               x))
%e A143375 Weaver determinant:
%e A143375 A0 = x^2;
%e A143375 B0 = x^5;
%e A143375 C0 = x^3;
%e A143375 D0 = x^7;
%e A143375 Expand[FullSimplify[ExpandAll[x^12*Det[{{-1, (1/B0 + 1/A0)}, {(1/D0 + 
               1/C0),
%e A143375 1/A0 + 1/B0 - 1}}]]]]
%t A143375 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}]
%Y A143375 Cf. A122762.
%Y A143375 Sequence in context: A004795 A161268 A007690 this_sequence A074364 A008796 
               A079966
%Y A143375 Adjacent sequences: A143372 A143373 A143374 this_sequence A143376 A143377 
               A143378
%K A143375 nonn,uned,probation
%O A143375 1,6
%A A143375 Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 
               22 2008

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