OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..375
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 640
FORMULA
E.g.f.: (1-x^4)/(1-x-x^4).
Recurrence: a(0)=1, a(1)=1, a(2)=2, a(3)=6, a(4)=24, a(n) = n*a(n-1) + n*(n-1)*(n-2)*(n-3)*a(n-4).
a(n) = (n!/283)*Sum_{alpha=RootOf(-1 +z +Z^4)} (36 - 9*alpha + 64*alpha^2 + 48*alpha^3)*alpha^(-1-n).
a(n) = n!*A003269(n), n>0. - R. J. Mathar, Nov 27 2011
MAPLE
spec := [S, {S=Sequence(Prod(Z, Sequence(Prod(Z, Z, Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
b[n_]:= b[n]= If[n<4, 1-Boole[n==0], b[n-1]+b[n-4]]; (* b = A003269 *)
a[n_]:= n!*b[n] +Boole[n==0];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jun 01 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( (1-x^4)/(1-x-x^4) ))); // G. C. Greubel, Jun 01 2022
(SageMath)
@CachedFunction
def A003269(n):
if (n<4): return 1-bool(n==0)
[A052692(n) for n in (0..40)] # G. C. Greubel, Jun 01 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved