A140876 Triangle T(n,k) = A053120(n+2,k)-2*A053120(n+1,k)+A053120(n,k) read by rows, 0<=k<n.

2, 0, 6, -2, 2, 16, 0, -10, 10, 40, 2, -2, -36, 36, 96, 0, 14, -14, -112, 112, 224, -2, 2, 64, -64, -320, 320, 512, 0, -18, 18, 240, -240, -864, 864, 1152, 2, -2, -100, 100, 800, -800, -2240, 2240, 2560, 0, 22, -22, -440, 440, 2464, -2464, -5632, 5632, 5632, -2, 2, 144, -144, -1680, 1680, 7168, -7168, -13824, 13824

Offset

1,1

Comments

Second differences downwards columns of the Chebyshev triangle A053120.

Row sums are 2, 6, 16, 40, 96, 224, 512, 1152, 2560, 5632, 12288,..., A057711.

Links

Table of n, a(n) for n=1..65.

Example

2;
0, 6;
-2, 2, 16;
0, -10, 10, 40;
2, -2, -36, 36, 96;
0, 14, -14, -112, 112, 224;
-2, 2, 64, -64, -320, 320, 512;
0, -18, 18, 240, -240, -864, 864, 1152;
2, -2, -100, 100, 800, -800, -2240, 2240, 2560;
0, 22, -22, -440, 440, 2464, -2464, -5632, 5632, 5632;
-2, 2, 144, -144, -1680, 1680, 7168, -7168, -13824, 13824, 12288;

Mathematica

Clear[T, D2, x, n, m] T[n_, m_] := CoefficientList[ChebyshevT[n + 1, x], x][[m + 1]]; D2[n_, m_] := T[n + 2, m] - 2*T[n + 1, m] + T[n, m]; a = Table[Flatten[Table[D2[n, m], {m, 0, n}]], {n, 0, 10}]; Flatten[a]

Crossrefs

Sequence in context: A143381 A322093 A277681 * A243997 A036044 A335790

Adjacent sequences: A140873 A140874 A140875 * A140877 A140878 A140879

Keyword

tabl,sign

Author

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

Status

approved