A158986 Coefficients of polynomials Q(n,x):=-2+(1+Q(n-1,x))^2, where Q(1,x)=x-2.

1, -2, 1, -2, -1, 1, -4, 4, 0, -2, 1, -8, 24, -32, 14, 8, -8, 0, -1, 1, -16, 112, -448, 1116, -1744, 1552, -384, -700, 736, -160, -128, 64, 0, 0, 0, -2, 1, -32, 480, -4480, 29112, -139552, 509600, -1441024, 3166616, -5345344, 6668992, -5473536, 1494624, 3005056, -4820608

Offset

1,2

Comments

Let P(n,x) be the n-th polynomial at A158984. Then Q(n,x)=P(n-1,x)-1 is a factor of P(n,x).

Links

Table of n, a(n) for n=1..51.

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

Example

Row 1: 1 -2 (from x-2)
Row 2: 1 -2 -1 (from x^2-2x-1)
Row 3: 1 -4 4 0 -2
Row 4: 1 -8 24 -32 14 8 -8 0 -1

Prog

(PARI) tabf(nn) = {p = x-2; print(Vec(p)); for (n=2, nn, p = -2 + (p+1)^2; print(Vec(p)); ); } \\ Michel Marcus, Mar 01 2016

Crossrefs

Cf. A158982, A158983, A158984, A158985.

Sequence in context: A083531 A003417 A358549 * A079900 A188317 A117354

Adjacent sequences: A158983 A158984 A158985 * A158987 A158988 A158989

Keyword

sign,tabf

Author

Clark Kimberling, Apr 02 2009

Status

approved