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Search: id:A140723
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| A140723 |
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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)). |
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1
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| 1, 1, -2, 2, -4, 4, -16, 0, 8, -16, 16, -14, -80, -48, 32, 32, -64, 64, 32, 0, -256, 0, 128, -256, -576, 0, 256, -912, 608, 1120, -1280, -1280, 512, 512
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{1, 1, 0, 0, -8, 0, -78, 0, -96, -576, -720};
Interesting effect here is that for primes:
p(x,n)=2^(Prime[n]-1)*(x-1).
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FORMULA
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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)).
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EXAMPLE
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{1},
{1},
{-2, 2},
{-4, 4},
{-16, 0, 8},
{-16, 16},
{-14, -80, -48, 32, 32},
{-64, 64},
{32, 0, -256, 0,128},
{-256, -576, 0, 256},
{-912, 608, 1120, -1280, -1280, 512, 512}
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A069947 A051547 A095329 this_sequence A106051 A066781 A112869
Adjacent sequences: A140720 A140721 A140722 this_sequence A140724 A140725 A140726
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KEYWORD
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tabf,uned,sign
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 12 2008
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