A228637 The number triangle associated with the polynomials V_n(x).

1, -1, 1, -1, 1, 1, 1, 1, 3, 1, 1, 1, 11, 5, 1, -1, 1, 41, 29, 7, 1, -1, 1, 153, 169, 55, 9, 1, 1, 1, 571, 985, 433, 89, 11, 1, 1, 1, 2131, 5741, 3409, 881, 131, 13, 1, -1, 1, 7953, 33461, 26839, 8721, 1561, 181, 15, 1

Offset: 0

Author

Jonny Griffiths, Aug 28 2013

Keywords

• sign
• tabl
• easy

Comments

V(n) is the polynomial with integer coefficients in x given by cos((2n+1)(arccos(x)/2))/(arccos(x)/2). The triangle here is given by V_0(0), V_1(0), V_0(1), V_2(0), V_1(1), V_0(2), V_3(0), V_2(1), V_1(2), V_0(3), V_4(0),....

Examples

			V_0(x)=1, V_1(x)=2x-1, V_2(x)=4x^2-2x-1,  ...
		

Crossrefs

Cf. A028297, A101124, A133156, A228161, A228565, A180870.

Formula

The terms are given by the recurrence relation V_{n+1}(x) = 2xV_n(x)-V_{n-1}(x), V_0(x) = 1, V_1(x)=2x-1.