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

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

Author

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

Keywords

• tabl
• sign

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.

Examples

			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;
		

Programs

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]