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A140877
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A triangular sequence based on second integer differential using columns n and rows m, in the ChebyshevT T(n,m): d20(n,m)=T(n+2,m)-2*T(n+1,m)+T(n,m); d02(n,m)=T(n,m+2)-2*T(n,m+1)+T(n,m); D2(n,m)=d20(n,m)+d02(n,m).
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0
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4, -7, 6, -8, -17, 4, 17, -22, -44, -16, 12, 51, -48, -120, -96, -31, 46, 146, -80, -336, -352, -16, -113, 140, 412, -64, -944, -1088, 49, -78, -372, 360, 1160, 224, -2624, -3072, 20, 211, -296, -1156, 784, 3264, 1536, -7168, -8192
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OFFSET
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1,1
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COMMENTS
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Row sums are:
{2, 6, 16, 40, 96, 224, 512, 1152, 2560, 5632, 12288};
The row type functions are empty for the first two.
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LINKS
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FORMULA
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d20(n,m)=T(n+2,m)-2*T(n+1,m)+T(n,m); d02(n,m)=T(n,m+2)-2*T(n,m+1)+T(n,m); D2(n,m)=d20(n,m)+d02(n,m).
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EXAMPLE
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{4},
{-7, 6},
{-8, -17, 4},
{17, -22, -44, -16},
{12, 51, -48, -120, -96},
{-31, 46, 146, -80, -336, -352},
{-16, -113, 140,412, -64, -944, -1088},
{49, -78, -372, 360, 1160, 224, -2624, -3072},
{20,211, -296, -1156, 784, 3264, 1536, -7168, -8192}
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MATHEMATICA
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Clear[T, D02, D20, D2, x, n, m] T[n_, m_] := CoefficientList[ChebyshevT[n + 1, x], x][[m + 1]]; D02[n_, m_] := If[m + 2 <= n, T[n, m + 2] - 2*T[n, m + 1] + T[n, m], {}]; D20[n_, m_] := T[n + 2, m] - 2*T[n + 1, m] + T[n, m]; D2[n_, m_] := D02[n, m] + D20[n, m]; a = Table[Flatten[Table[D2[n, m], {m, 0, n}]], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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