|
Search: id:A162514
|
|
|
| A162514 |
|
Triangle of coefficients of polynomials defined by Binet form: P(n,x) = U^n+L^n, where U=(x+d)/2, L=(x-d)/2, d=(4 + x^2)^(1/2). |
|
+0
4
|
|
| 2, 1, 0, 1, 0, 2, 1, 0, 3, 0, 1, 0, 4, 0, 2, 1, 0, 5, 0, 5, 0, 1, 0, 6, 0, 9, 0, 2, 1, 0, 7, 0, 14, 0, 7, 0, 1, 0, 8, 0, 20, 0, 16, 0, 2, 1, 0, 9, 0, 27, 0, 30, 0, 9, 0, 1, 0, 10, 0, 35, 0, 50, 0, 25, 0, 2, 1, 0, 11, 0, 44, 0, 77, 0, 55, 0, 11, 0, 1, 0, 12, 0, 54, 0, 112, 0, 105, 0, 36, 0, 2, 1, 0, 13, 0
(list; table; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Row sums 2,1,3,4,7,... are the Lucas numbers, A000032.
|
|
FORMULA
|
P(n,x)=x*P(n-1,x)+P(n-2,x).
|
|
EXAMPLE
|
First six rows:
2
1...0
1...0...2
1...0...3...0
1...0...4...0...2
1...0...5...0...5...0
|
|
CROSSREFS
|
A000032, A162515, A162516, A162517
Sequence in context: A115672 A079694 A068906 this_sequence A166347 A055300 A156256
Adjacent sequences: A162511 A162512 A162513 this_sequence A162515 A162516 A162517
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu), Jul 05 2009
|
|
|
Search completed in 0.002 seconds
|
