|
Search: id:A052963
|
|
|
| A052963 |
|
a(0)=1, a(1)=2, a(2)=5, a(n) = 3*a(n+2) - a(n+3). |
|
+0
2
|
|
| 1, 2, 5, 14, 40, 115, 331, 953, 2744, 7901, 22750, 65506, 188617, 543101, 1563797, 4502774, 12965221, 37331866, 107492824, 309513251, 891207887, 2566130837, 7388879260, 21275429893, 61260158842, 176391597266, 507899361905
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
A simple regular expression.
|
|
LINKS
|
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1034
|
|
FORMULA
|
G.f.: -(-1+x+x^2)/(1-3*x+x^3)
Sum(1/9*(1+2*_alpha+_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z+_Z^3))
a(n)/a(n-1) tends to 2.8793852... = 2Cos(4)Pi/9, a root of x^3 -3x^2 + 1 (the characteristic polynomial of the 3 X 3 matrix). The latter polynomial is a factor (with (x + 1)) of the 4th degree polynomial of A066170: x^4 - 2x^3 - 3x^2 + x + 1. Given the 3 X 3 matrix [0 1 0 / 0 0 1 / -1 0 3], (M^n)*[1 1 1] = [a(n-2), a(n-1), a(n)]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 29 2004
|
|
MAPLE
|
spec := [S, {S=Sequence(Union(Prod(Sequence(Union(Prod(Z, Z), Z)), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
|
|
CROSSREFS
|
Cf. A066170.
Sequence in context: A081908 A059505 A117189 this_sequence A036908 A126220 A136304
Adjacent sequences: A052960 A052961 A052962 this_sequence A052964 A052965 A052966
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000
|
|
|
Search completed in 0.002 seconds
|
