Search: id:A143389
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%I A143389
%S A143389 1,3,3,1,6,7,1,9,11,7,34,32,23,95,99,27,219,250,76,571,619,241,1517,
%T A143389 1684,511,3927,4500,1205,10120,11628,3041
%V A143389 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,
%W A143389 -3927,4500,1205,-10120,11628,3041
%N A143389 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.
%D A143389 Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, 
               University of Illinois Press, Chicago, 1963, p37 - 38
%F A143389 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)).
%e A143389 Weaver determinant:
%e A143389 A0 = Cyclotomic[2, x]
%e A143389 B0 = Cyclotomic[5, x]
%e A143389 C0 = Cyclotomic[3, x]
%e A143389 D0 = Cyclotomic[7, x]
%e A143389 Expand[FullSimplify[ExpandAll[((1 + x) (1 + x + x^2) (
%e A143389 1 + x + x^2 + x^3 + x^4) (
%e A143389 1 + x + x^2 + x^3 + x^4 + x^5 + x^6))*Det[{{-1, (1/B0 + 1/A0)}, {(1/
%e A143389 D0 + 1/C0),
%e A143389 1/A0 + 1/B0 - 1}}]]]]
%p A143389 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}]
%Y A143389 Sequence in context: A010468 A082009 A110640 this_sequence A094040 A039798 
               A001498
%Y A143389 Adjacent sequences: A143386 A143387 A143388 this_sequence A143390 A143391 
               A143392
%K A143389 uned,probation,sign
%O A143389 1,2
%A A143389 Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 
               22 2008

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