|
|
A123222
|
|
Expansion of -x * (x-1) * (3*x^2-1) / (9*x^4-8*x^3+4*x-1).
|
|
0
|
|
|
1, 3, 9, 31, 109, 391, 1397, 4995, 17833, 63675, 227313, 811543, 2897269, 10343647, 36928061, 131837979, 470678161, 1680380979, 5999172633, 21417807055, 76464283837, 272987183095, 974598829637, 3479441311347, 12422046335161
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 4*a(n-1) -8*a(n-3) +9*a(n-4).
G.f.: -x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1). (End)
|
|
MAPLE
|
seq(coeff(series(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1), x, n+1), x, n), n = 1 .. 25); # Muniru A Asiru, Oct 13 2018
|
|
MATHEMATICA
|
LinearRecurrence[{4, 0, -8, 9}, {1, 3, 9, 31}, 30] (* Harvey P. Dale, Jul 26 2018 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1)) \\ G. C. Greubel, Oct 12 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1))); // G. C. Greubel, Oct 12 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,less
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|