A140883 Triangle T(n,k) = A053120(n,k)+A053120(n,n-k) of symmetrized Chebyshev coefficients, read by rows, 0<=k<=n.

2, 1, 1, 1, 0, 1, 4, -3, -3, 4, 9, 0, -16, 0, 9, 16, 5, -20, -20, 5, 16, 31, 0, -30, 0, -30, 0, 31, 64, -7, -112, 56, 56, -112, -7, 64, 129, 0, -288, 0, 320, 0, -288, 0, 129, 256, 9, -576, -120, 432, 432, -120, -576, 9, 256, 511, 0, -1230, 0, 720, 0, 720, 0, -1230, 0, 511

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Jul 22 2008

Keywords

• tabl
• sign

Comments

Row sums are constantly two.

Examples

			2;
1, 1;
1, 0, 1;
4, -3, -3, 4;
9, 0, -16, 0, 9;
16, 5, -20, -20, 5, 16;
31, 0, -30, 0, -30, 0, 31;
64, -7, -112, 56, 56, -112, -7, 64;
129, 0, -288, 0, 320, 0, -288, 0, 129;
256, 9, -576, -120, 432, 432, -120, -576, 9, 256;
511, 0, -1230, 0, 720, 0, 720, 0, -1230, 0, 511;
		

Crossrefs

Cf. A053120.

Programs

Mathematica

Clear[p, x, n, m, a]; p[x_, n_] := ChebyshevT[n, x] + ExpandAll[x^n*ChebyshevT[n, 1/x]]; Table[p[x, n], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]

Formula

T(n,k) = T(n,n-k).