login
A052990
Expansion of ( 1-x ) / ( 1-4*x-x^2+2*x^3 ).
1
1, 3, 13, 53, 219, 903, 3725, 15365, 63379, 261431, 1078373, 4448165, 18348171, 75684103, 312188253, 1287740773, 5311783139, 21910496823, 90378288885, 372800086085, 1537757639579, 6343074066631, 26164453733933, 107925373723205, 445179800493491
OFFSET
0,2
FORMULA
G.f.: (1-x)/(1-4*x-x^2+2*x^3)
Recurrence: {a(0)=1, a(1)=3, a(2)=13, 2*a(n)-a(n+1)-4*a(n+2)+a(n+3)=0}
Sum(-1/142*(-22+18*r^2-21*r)*r^(-1-n) where r=RootOf(1-4*_Z-_Z^2+2*_Z^3))
MAPLE
spec := [S, {S=Sequence(Union(Prod(Union(Sequence(Z), Z), Union(Z, Z)), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
MATHEMATICA
LinearRecurrence[{4, 1, -2}, {1, 3, 13}, 40] (* Vincenzo Librandi, Jun 23 2012 *)
CoefficientList[Series[(1-x)/(1-4x-x^2+2x^3), {x, 0, 40}], x] (* Harvey P. Dale, Jan 15 2022 *)
PROG
(Magma) I:=[1, 3, 13]; [n le 3 select I[n] else 4*Self(n-1)+Self(n-2)-2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 23 2012
CROSSREFS
Sequence in context: A342815 A072197 A065838 * A151209 A151210 A151211
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved