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A162517 Triangle of coefficients of polynomials defined by Binet form: P(n,x) = (U^n-L^n)/(2d), where U=x+d, L=x-d, d=(x+4)^(1/2). 11
0, 1, 2, 0, 3, 1, 4, 4, 4, 16, 0, 5, 10, 41, 8, 16, 6, 20, 86, 48, 96, 0, 7, 35, 161, 169, 348, 48, 64, 8, 56, 280, 456, 992, 384, 512, 0, 9, 84, 462, 1044, 2449, 1744, 2400, 256, 256, 10, 120, 732, 2136, 5482, 5920, 8640, 2560, 2560, 0, 11, 165, 1122, 4026, 11407 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..61.

FORMULA

P(n,x)=2x*P(n-1,x)-(x^2-x-4)*P(n-2,x).

Let Q(n,x) be the n-th polynomial at A162516; then

Q(n,x)=P(n+1,x)-x*P(n,x).

EXAMPLE

First six rows:

0

1

2...0

3...1...4

4...4...16...0

5...10..41...8...16

CROSSREFS

A162514, A162515, A162516.

Sequence in context: A053445 A175990 A290982 * A180876 A162170 A266770

Adjacent sequences:  A162514 A162515 A162516 * A162518 A162519 A162520

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 05 2009

STATUS

approved

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Last modified October 20 07:23 EDT 2019. Contains 328252 sequences. (Running on oeis4.)