A140723 - OEIS

%I #2 Oct 12 2012 14:54:50

%S 1,1,-2,2,-4,4,-16,0,8,-16,16,-14,-80,-48,32,32,-64,64,32,0,-256,0,

%T 128,-256,-576,0,256,-912,608,1120,-1280,-1280,512,512

%N A triangular sequence of coefficients of a truncated quotient (remainder dropped) of the ChebyshevT polynomials T(x,n) by the Cyclotomic polynomials c(x,n): p(x,n)=Quotient(T(x.n)/c(x,n)).

%C Row sums are:

%C {1, 1, 0, 0, -8, 0, -78, 0, -96, -576, -720};

%C Interesting effect here is that for primes:

%C p(x,n)=2^(Prime[n]-1)*(x-1).

%F ChebyshevT polynomials T(x,n): Cyclotomic polynomials c(x,n): p(x,n)=Quotient(T(x.n)/c(x,n)) a(n,m)=Coefficients(p(x,n)).

%e {1},

%e {1},

%e {-2, 2},

%e {-4, 4},

%e {-16, 0, 8},

%e {-16, 16},

%e {-14, -80, -48, 32, 32},

%e {-64, 64},

%e {32, 0, -256, 0,128},

%e {-256, -576, 0, 256},

%e {-912, 608, 1120, -1280, -1280, 512, 512}

%t Clear[p, x, n, a] p[x_, n_] = PolynomialQuotient[ChebyshevT[n, x], Cyclotomic[n, x], x]; Table[p[x, n], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]

%K tabf,uned,sign

%O 1,3

%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 12 2008