OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1054
Index entries for linear recurrences with constant coefficients, signature (4,3,-3)
FORMULA
G.f.: (1-x)/(1-4*x-3*x^2+3*x^3).
Recurrence: {a(0)=1, a(1)=3, a(2)=15, 3*a(n)-3*a(n+1)-4*a(n+2)+a(n+3)=0}.
Sum(-1/95*(-11-22*r+15*r^2)*r^(-1-n) where r=RootOf(1-4*_Z-3*_Z^2+3*_Z^3)).
MAPLE
spec:= [S, {S=Sequence(Prod(Union(Z, Z, Z), Union(Sequence(Z), Z)))}, unlabeled]: seq(combstruct[count ](spec, size=n), n=0..20);
MATHEMATICA
LinearRecurrence[{4, 3, -3}, {1, 3, 15}, 40] (* Vincenzo Librandi, Jun 23 2012 *)
CoefficientList[Series[(1-x)/(1-4x-3x^2+3x^3), {x, 0, 30}], x] (* Harvey P. Dale, Jun 07 2024 *)
PROG
(Magma) I:=[1, 3, 15]; [n le 3 select I[n] else 4*Self(n-1)+3*Self(n-2) -3*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 23 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved