A158982 Coefficients of polynomials P(n,x):=-2+P(n-1,x)^2, where P(0,x)=x-2.

1, -2, 1, -4, 2, 1, -8, 20, -16, 2, 1, -16, 104, -352, 660, -672, 336, -64, 2, 1, -32, 464, -4032, 23400, -95680, 283360, -615296, 980628, -1136960, 940576, -537472, 201552, -45696, 5440, -256, 2, 1, -64, 1952, -37760, 520144, -5430656, 44662464

Offset

1,2

Comments

The 2^n zeros of P(n,x) are 2+2*cos[(2k-1)Pi/(2^(n+1))], k=1,2,...,2^n.

P(n,x) = 2*T(2^(n+1),(1/2)x^(1/2)), where T(k,t) is the k-th Chebyshev polynomial of the first kind.

Links

Table of n, a(n) for n=1..43.

Clark Kimberling, Polynomials defined by a second-order recurrence, interlacing zeros, and Gray codes, The Fibonacci Quarterly 48 (2010) 209-218.

Formula

P(n+1,x+2) = P(n,x^2) for n>=0.

Example

Row 1: 1 -2 (from x-2)
Row 2: 1 -4 2 (from x^2-4x+2)
Row 3: 1 -8 20 -16 2
Row 4: 1 -16 104 -352 660 -672 336 -64 2

Prog

(PARI) tabf(nn) = {p = x-2; print(Vec(p)); for (n=2, nn, p = -2 + p^2; print(Vec(p)); ); } \\ Michel Marcus, Mar 01 2016

Crossrefs

Cf. A084534, A158983, A158984, A158985, A158986.

Sequence in context: A158264 A274106 A354802 * A127124 A127136 A239101

Adjacent sequences: A158979 A158980 A158981 * A158983 A158984 A158985

Keyword

sign,tabf

Author

Clark Kimberling, Apr 02 2009

Status

approved