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%I #4 Oct 12 2012 14:54:53
%S 1,-1,1,1,2,1,1,2,2,1,1,2,2,2,1,1,2,2,2,2,1,1,3,3,2,3,3,1,1,2,2,2,2,2,
%T 2,1,1,4,6,4,2,4,6,4,1,1,3,3,2,3,3,2,3,3,1,1,5,10,10,5,2,5,10,10,5,1
%N A "completed" set of cyclotomic polynomial with coefficients that are a triangular sequence: ( filled out with powers of (x+1)^m) p(x,n)=If[PrimeQ[n], Cyclotomic[n, x]*(x + 1), Cyclotomic[n, x]*(x + 1)^(n + 1 - Length[CoefficientList[Cyclotomic[n, x], x]])];.
%C Row sums are:
%C {1, 0, 4, 6, 8, 10, 16, 14, 32, 24, 64}.
%C The problem with Cyclotomic polynomials is there uneven lengths:
%C Here roots of -1 as (x+1) powers are used to fill out the triangle with positive coefficients.
%F p(x,n)=If[PrimeQ[n], Cyclotomic[n, x]*(x + 1), Cyclotomic[n, x]*(x + 1)^(n + 1 - Length[CoefficientList[Cyclotomic[n, x], x]])]; t(n,m)=Coefficients(p)x,n))
%e {1},
%e {-1, 1},
%e {1, 2, 1},
%e {1, 2, 2, 1},
%e {1, 2, 2, 2, 1},
%e {1, 2, 2, 2, 2, 1},
%e {1, 3, 3, 2, 3, 3, 1},
%e {1, 2, 2, 2, 2, 2, 2, 1},
%e {1, 4, 6, 4, 2, 4, 6, 4, 1},
%e {1, 3, 3, 2, 3, 3, 2, 3, 3, 1},
%e {1, 5, 10, 10, 5, 2, 5, 10, 10, 5, 1}
%t p[x_, n_] := If[PrimeQ[n],Cyclotomic[n, x]*(x + 1), Cyclotomic[n, x]*(x + 1)^(n + 1 - Length[CoefficientList[Cyclotomic[n, x], x]])]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
%K uned,sign
%O 1,5
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 20 2008
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