|
| |
|
|
A014991
|
|
a(n) = (1 - (-9)^n)/10.
|
|
8
|
|
|
|
1, -8, 73, -656, 5905, -53144, 478297, -4304672, 38742049, -348678440, 3138105961, -28242953648, 254186582833, -2287679245496, 20589113209465, -185302018885184, 1667718169966657, -15009463529699912
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
q-integers for q = -9.
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (-8,9).
|
|
|
FORMULA
|
a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
a(0)=1, a(1)=-8, a(n) = -8*a(n-1) + 9*a(n-2). - Harvey P. Dale, Aug 08 2011
G.f.: x/((1 - x)*(1 + 9*x)). - Vincenzo Librandi, Oct 22 2012
E.g.f.: (exp(x) - exp(-9*x))/10. - G. C. Greubel, May 26 2018
|
|
|
MAPLE
|
a:=n->sum ((-9)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008
|
|
|
MATHEMATICA
|
((-9)^Range[30]-1)/-10 (* or *) LinearRecurrence[{-8, 9}, {1, -8}, 30] (* Harvey P. Dale, Aug 08 2011 *)
CoefficientList[Series[1/((1 - x)*(1 + 9*x)), {x, 0, 30}], x]; (* Vincenzo Librandi, Oct 22 2012 *)
|
|
|
PROG
|
(Sage) [gaussian_binomial(n, 1, -9) for n in range(1, 19)] # Zerinvary Lajos, May 28 2009
(Magma) I:=[1, -8]; [n le 2 select I[n] else -8*Self(n-1)+9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012
(PARI) for(n=1, 30, print1((1-(-9)^n)/10, ", ")) \\ G. C. Greubel, May 26 2018
|
|
|
CROSSREFS
|
Cf. A077925, A014983, A014985-A014987, A014989-A014994. - Zerinvary Lajos, Dec 16 2008
Sequence in context: A282786 A241630 A153482 * A015577 A293151 A082764
Adjacent sequences: A014988 A014989 A014990 * A014992 A014993 A014994
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
Olivier Gérard
|
|
|
EXTENSIONS
|
Better name from Ralf Stephan, Jul 14 2013
|
|
|
STATUS
|
approved
|
| |
|
|
