|
|
A165206
|
|
a(n) = (3-4*n)*F(2*n-2) + (4-7*n)*F(2*n-1).
|
|
2
|
|
|
1, -3, -25, -112, -416, -1411, -4537, -14085, -42653, -126794, -371554, -1076423, -3089555, -8799207, -24897121, -70052356, -196151492, -546916555, -1519249933, -4206274089, -11611243109, -31967026718, -87796880710
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1-9*x+4*x^2-x^3)/(1-3*x+x^2)^2 = (1-x)/(1-3*x+x^2) - 5*x/(1-3*x+x^2)^2.
|
|
MATHEMATICA
|
Table[(3-4n)Fibonacci[2n-2]+(4-7n)Fibonacci[2n-1], {n, 0, 30}] (* or *) LinearRecurrence[{6, -11, 6, -1}, {1, -3, -25, -112}, 30] (* Harvey P. Dale, Aug 25 2013 *)
|
|
PROG
|
(PARI) vector(30, n, n--; f=fibonacci; (3-4*n)*f(2*n-2)+(4-7*n)*f(2*n-1)) \\ G. C. Greubel, Jul 18 2019
(Magma) F:=Fibonacci; [(3-4*n)*F(2*n-2)+(4-7*n)*F(2*n-1): n in [0..30]]; // G. C. Greubel, Jul 18 2019
(Sage) f=fibonacci; [(3-4*n)*f(2*n-2)+(4-7*n)*f(2*n-1) for n in (0..30)] # G. C. Greubel, Jul 18 2019
(GAP) F:=Fibonacci;; List([0..30], n-> (3-4*n)*F(2*n-2)+(4-7*n)*F(2*n-1) ); # G. C. Greubel, Jul 18 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|