|
| |
|
|
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).
|
|
4
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
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: A008734 A053445 A175990 * A180876 A162170 A008798
Adjacent sequences: A162514 A162515 A162516 * A162518 A162519 A162520
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Jul 05 2009
|
| |
|
|
