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%I #6 Dec 30 2012 01:38:03
%S 4,-7,6,-8,-17,4,17,-22,-44,-16,12,51,-48,-120,-96,-31,46,146,-80,
%T -336,-352,-16,-113,140,412,-64,-944,-1088,49,-78,-372,360,1160,224,
%U -2624,-3072,20,211,-296,-1156,784,3264,1536,-7168,-8192
%N 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).
%C Row sums are:
%C {2, 6, 16, 40, 96, 224, 512, 1152, 2560, 5632, 12288};
%C The row type functions are empty for the first two.
%F 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).
%e {4},
%e {-7, 6},
%e {-8, -17, 4},
%e {17, -22, -44, -16},
%e {12, 51, -48, -120, -96},
%e {-31, 46, 146, -80, -336, -352},
%e {-16, -113, 140,412, -64, -944, -1088},
%e {49, -78, -372, 360, 1160, 224, -2624, -3072},
%e {20,211, -296, -1156, 784, 3264, 1536, -7168, -8192}
%t 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]
%K uned,tabl,sign
%O 1,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 21 2008