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A140885 Triangle T(n,k) read by rows: the coefficient [x^k] ( Phi(n,x)+x^n*Phi(n,1/x)) related to cyclotomic polynomials Phi(n,x). 0

%I #5 Oct 12 2012 14:54:50

%S 0,0,0,1,2,1,1,2,2,1,1,0,2,0,1,1,2,2,2,2,1,1,-1,1,0,1,-1,1,1,2,2,2,2,

%T 2,2,1,1,0,0,0,2,0,0,0,1,1,0,0,2,0,0,2,0,0,1,1,-1,1,-1,1,0,1,-1,1,-1,

%U 1,1,2,2,2,2,2,2,2,2,2,2,1,1,0,-1,0,1,0,0,0,1,0,-1,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,1,1,-1,1

%N Triangle T(n,k) read by rows: the coefficient [x^k] ( Phi(n,x)+x^n*Phi(n,1/x)) related to cyclotomic polynomials Phi(n,x).

%C Row sums are: 0, 0, 4, 6, 4, 10, 2, 14, 4, 6, 2, 22, 2, 26, 2, 2, 4, 34, 2, 38, 2,...

%F T(n,k) = T(n,n-k) .

%e 0; # x+x^0*(1/x) = x+1/x

%e 0, 0; # x-1+x*(1/x-1) = 0

%e 1, 2, 1; # x+1+x^2*(1/x+1) = 1+2*x+x^2

%e 1, 2, 2, 1;

%e 1, 0, 2, 0, 1;

%e 1, 2, 2, 2, 2, 1;

%e 1, -1, 1, 0, 1, -1, 1;

%e 1, 2, 2, 2, 2, 2, 2, 1;

%e 1, 0, 0, 0, 2, 0, 0, 0, 1;

%e 1, 0, 0, 2, 0, 0, 2, 0, 0, 1;

%e 1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1;

%t Clear[p, x, n, m, a]; p[x_, n_] := Cyclotomic[n, x] + ExpandAll[x^n*Cyclotomic[n, 1/x]]; Table[p[x, n], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]

%Y Cf. A013595.

%K tabl,sign

%O 0,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 22 2008

%E All entries replaced to comply with the definition and examples - The Assoc. Eds. of the OEIS, Oct 12 2010

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)