A052976 Expansion of (1-2x)/(1-3x-x^3+2x^4).

1, 1, 3, 10, 29, 88, 268, 813, 2469, 7499, 22774, 69165, 210056, 637944, 1937449, 5884073, 17870051, 54271714, 164824317, 500574856, 1520256180, 4617049429, 14022074509, 42585329995, 129332527054, 392785556813, 1192897851416

Offset

0,3

Links

Table of n, a(n) for n=0..26.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1048

Index entries for linear recurrences with constant coefficients, signature (3,0,1,-2).

Formula

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

Recurrence: {a(1)=1, a(0)=1, a(2)=3, a(3)=10, 2*a(n)-a(n+1)-3*a(n+3)+a(n+4)=0}

Sum(-1/9247*(-382-2063*_alpha+26*_alpha^2+552*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-_Z^3+2*_Z^4))

Maple

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

Mathematica

CoefficientList[Series[(1-2x)/(1-3x-x^3+2x^4), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, 0, 1, -2}, {1, 1, 3, 10}, 40] (* Harvey P. Dale, Nov 02 2013 *)

Crossrefs

Sequence in context: A291393 A244615 A307062 * A361365 A147363 A147226

Adjacent sequences: A052973 A052974 A052975 * A052977 A052978 A052979

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 06 2000

Status

approved