A052994 Expansion of 2x(1-x)/(1-2x-x^2+x^3).

0, 2, 2, 6, 12, 28, 62, 140, 314, 706, 1586, 3564, 8008, 17994, 40432, 90850, 204138, 458694, 1030676, 2315908, 5203798, 11692828, 26273546, 59036122, 132652962, 298068500, 669753840, 1504923218, 3381531776, 7598232930, 17073074418

Offset

0,2

Links

Table of n, a(n) for n=0..30.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1071

Sergey Kitaev, Jeffrey Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.

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

Formula

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

Recurrence: {a(0)=0, a(1)=2, a(2)=2, a(n)-a(n+1)-2*a(n+2)+a(n+3)=0}

Sum(2/7*(-_alpha+_alpha^2+1)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))

Maple

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

Prog

(PARI) concat(0, Vec(-2*x*(-1+x)/(x^3-x^2-2*x+1) + O(x^40))) \\ Michel Marcus, Mar 19 2015

Crossrefs

Equals 2 * A006356(n-2), n>1.

Sequence in context: A115962 A019311 A216215 * A088219 A027375 A059727

Adjacent sequences: A052991 A052992 A052993 * A052995 A052996 A052997

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 05 2000

Status

approved