A052903 Expansion of (1-x^3)/(1-2x-x^3+x^4).

1, 2, 4, 8, 17, 36, 76, 161, 341, 722, 1529, 3238, 6857, 14521, 30751, 65121, 137906, 292042, 618454, 1309693, 2773522, 5873456, 12438151, 26340131, 55780196, 118125087, 250152154, 529744373, 1121833637, 2375694341, 5030980901

Offset

0,2

Comments

Partial sums of A052908. - R. J. Mathar, Nov 28 2011

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 881

Index entries for linear recurrences with constant coefficients, signature (2,0,1,-1)

Formula

G.f.: -(-1+x^3)/(1-2*x-x^3+x^4)

Recurrence: {a(0)=1, a(2)=4, a(1)=2, a(3)=8, a(n)-a(n+1)-2*a(n+3)+a(n+4)=0}

Sum(-1/643*(-222-40*_alpha-93*_alpha^2+54*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-_Z^3+_Z^4))

a(n) = A052908(n)-A052908(n-3), n>3. - R. J. Mathar, Apr 26 2017

Maple

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

Mathematica

CoefficientList[Series[(1-x^3)/(1-2x-x^3+x^4), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 0, 1, -1}, {1, 2, 4, 8}, 40] (* Harvey P. Dale, Jul 21 2021 *)

Crossrefs

Sequence in context: A247297 A292322 A008999 * A308745 A226729 A063457

Adjacent sequences: A052900 A052901 A052902 * A052904 A052905 A052906

Keyword

easy,nonn

Author

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

Status

approved