A140877 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).

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

Offset

1,1

Comments

Row sums are:

{2, 6, 16, 40, 96, 224, 512, 1152, 2560, 5632, 12288};

The row type functions are empty for the first two.

Links

Table of n, a(n) for n=1..45.

Formula

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).

Example

{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}

Mathematica

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]

Crossrefs

Sequence in context: A200353 A081845 A254339 * A293904 A069286 A079354

Adjacent sequences: A140874 A140875 A140876 * A140878 A140879 A140880

Keyword

uned,tabl,sign

Author

Roger L. Bagula and Gary W. Adamson, Jul 21 2008

Status

approved