|
|
A052965
|
|
Expansion of (1-x)/(1-3x-4x^2+4x^3).
|
|
0
|
|
|
1, 2, 10, 34, 134, 498, 1894, 7138, 26998, 101970, 385350, 1455938, 5501334, 20786354, 78540646, 296762018, 1121303222, 4236795154, 16008550278, 60487618562, 228549876182, 863565901682, 3262946735526, 12328904308578
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -(-1+x)/(1-3*x-4*x^2+4*x^3)
Recurrence: {a(0)=1, a(1)=2, a(2)=10, 4*a(n)-4*a(n+1)-3*a(n+2)+a(n+3)=0}
Sum(-1/158*(-17-49*_alpha+40*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-4*_Z^2+4*_Z^3))
|
|
MAPLE
|
spec := [S, {S=Sequence(Prod(Union(Z, Z, Sequence(Z)), Union(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
|
|
MATHEMATICA
|
CoefficientList[Series[(1-x)/(1-3x-4x^2+4x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, 4, -4}, {1, 2, 10}, 40] (* Harvey P. Dale, Dec 01 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|