OFFSET
0,5
COMMENTS
Compare the definition of U_n(x) with the definition of the Dirichlet kernel.
U_n(x) is defined as sin((n+1)arccos(x))/sin(arccos(x)).
U_n(x) is a polynomial in x with integer coefficients for all n >=0.
The initial term is U_0(0).
The triangle is given here as U_0(0), U_1(0), U_1(1), U_2(0), U_2(1), U(2)_(2), U_3(0),....
LINKS
T. D. Noe, Rows n = 0..100 of triangle, flattened
Wikipedia, Chebyshev polynomials
FORMULA
The polynomials can be computed with U_{n+1}(x) = 2xU_n(x) - U_{n-1}(x), U_{n+1}(x) = ((U_n(x))^2-1)/U_{n-1)(x), where in each case U_0(x) = 1; U_1(x) = 2x.
MATHEMATICA
nn = 10; Flatten[Table[ChebyshevU[i - j, j], {i, 0, nn}, {j, 0, i}]] (* T. D. Noe, Aug 16 2013 *)
CROSSREFS
KEYWORD
AUTHOR
Jonny Griffiths, Aug 14 2013
STATUS
approved