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Search: id:A123027
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| A123027 |
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A053122(n,m)=CoefficientList(ChebyshevU[n, x/2 - 1]): triangular array made from Bezier transform of A053122. |
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+0
1
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| 1, -2, 3, 3, -10, 8, -4, 22, -38, 21, 5, -40, 111, -130, 55, -6, 65, -256, 474, -420, 144, 7, -98, 511, -1324, 1836, -1308, 377, -8, 140, -924, 3130, -6020, 6666, -3970, 987, 9, -192, 1554, -6588, 16435, -25088, 23109, -11822, 2584, -10, 255, -2472, 12720, -39430, 77645, -98160, 77378, -34690, 6765, 11, -330
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Alternative Adamson Matrix method: T[n_, m_] = If[ n == m, 2, If[n == m - 1 || n == m + 1, 1, 0]]; M[d_] := Table[T[n, m], {n, 1, d}, {m, 1, d}]; Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[{{1}}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; b = Table[CoefficientList[Sum[a[[m + 1]][[n + 1]]*x^n*(1 - x)^(m - n), {n, 0, m}], x], {m, 0, 10}]; Flatten[b]
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FORMULA
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T(n,m)=A053122(n,m) T'(n,m)=t(n,m)*x^n*(1-x)^(m-n)
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EXAMPLE
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1
-2, 3
3, -10, 8,
-4, 22, 38, 21
5, -40, 111, -130, 55
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MATHEMATICA
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b0 = Table[CoefficientList[ExpandAll[ChebyshevU[n, x/2 - 1]], x], {n, 0, 10}]; c0 = Table[CoefficientList[Sum[b0[[m + 1]][[n + 1]]*x^n*(1 - x)^(m - n), {n, 0, m}], x], {m, 0, 10}]; Flatten[c0]
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CROSSREFS
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Cf. A053122.
Adjacent sequences: A123024 A123025 A123026 this_sequence A123028 A123029 A123030
Sequence in context: A124931 A124932 A110042 this_sequence A100652 A094416 A152300
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KEYWORD
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sign,uned,tabl
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 24 2006
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