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A052911 Expansion of (1-x)/(1-3x-x^2+2x^3). 3
1, 2, 7, 21, 66, 205, 639, 1990, 6199, 19309, 60146, 187349, 583575, 1817782, 5662223, 17637301, 54938562, 171128541, 533049583, 1660400166, 5171992999, 16110279997, 50182032658, 156312391973, 486898648583, 1516644272406 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 891

Index entries for linear recurrences with constant coefficients, signature (3,1,-2).

FORMULA

G.f.: -(-1+x)/(1-3*x-x^2+2*x^3)

2*a(n)-a(n+1)-3*a(n+2)+a(n+3)=0.

Sum(-1/229*(-43-41*_alpha+46*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-_Z^2+2*_Z^3))

a(n) = center term in M^n * [1 1 1] where M = Hosoya's triangle considered as an upper triangular 3 X 3 matrix: [2 1 2 / 1 1 0 / 1 0 0]. E.g. a(4) = 66 since M^4 * [1 1 1] = [139 66 45]. The analogous procedure using M^n * [1 0 0] generates A100058. - Gary W. Adamson, Oct 31 2004

a(n) = A100058(n) - A100058(n-1). - R. J. Mathar, May 04 2018

MAPLE

spec := [S, {S=Sequence(Union(Z, Prod(Union(Sequence(Z), Z, Z), Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

CROSSREFS

Cf. A100058, A058071, A100059.

Sequence in context: A027990 A037520 A218836 * A126133 A186240 A274203

Adjacent sequences:  A052908 A052909 A052910 * A052912 A052913 A052914

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

More terms from James A. Sellers, Jun 06 2000

STATUS

approved

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Last modified October 14 08:54 EDT 2019. Contains 327995 sequences. (Running on oeis4.)