|
| |
|
|
A080097
|
|
Fibonacci(n+2)^2 - 1.
|
|
8
| |
|
|
0, 3, 8, 24, 63, 168, 440, 1155, 3024, 7920, 20735, 54288, 142128, 372099, 974168, 2550408, 6677055, 17480760, 45765224, 119814915, 313679520, 821223648, 2149991423, 5628750624, 14736260448, 38580030723, 101003831720
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| a(n), a(n)+1 and a(n)+2 are consecutive members of A049997.
|
|
|
FORMULA
| If n is odd, then a(n) = F(n+1)F(n+3) = F(n)F(n+4)-2, else a(n) = F(n)F(n+4) = F(n+1)F(n+3)-2, where F(n) = Fibonacci numbers (A000045).
(1/5) {Lucas(2n+4) - 2(-1)^n - 5}.
G.f.: (3x+2x^2-x^3)/(1-x^2)(1-2x-2x^2+x^3)).
|
|
|
MATHEMATICA
| CoefficientList[Series[(3x+2x^2-x^3)/(1-x^2)(1-2x-2x^2+x^3)), {x, 0, 35}], x]
Table[Fibonacci[(n+2)]^2-1, {n, 0, 100}] (*From Vladimir Joseph Stephan Orlovsky, Apr 03 2011*)
|
|
|
CROSSREFS
| Equals A007598(n+2) - 1. Cf. A064831, A059840.
Sequence in context: A084920 A026556 A096001 * A096886 A176904 A056332
Adjacent sequences: A080094 A080095 A080096 * A080098 A080099 A080100
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Jan 29 2003
|
|
|
EXTENSIONS
| Edited by Ralf Stephan, May 15 2005
|
| |
|
|
