OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250 (terms n = 0..60 from Ray Chandler)
A. Baxter, B. Nakamura, and D. Zeilberger. Automatic generation of theorems and proofs on enumerating consecutive Wilf-classes
V. Dotsenko and A. Khoroshkin, Shuffle algebras, homology, and consecutive pattern avoidance, arXiv preprint arXiv:1109.2690, 2011
FORMULA
The reference gives an e.g.f. There is an associated triangle of numbers c_{n,l} that should be added to the OEIS if it is not already present.
a(n) ~ c * d^n * n!, where d = 0.95482605094987833345080179991528996596888600981..., c = 1.1567436851576902067739566662625378535625602... . - Vaclav Kotesovec, Sep 11 2014
MAPLE
c := proc(n, l)
if n = 1 then
if l = 0 then
1;
else
0;
end if;
elif n= 2 or n = 3 then
0;
else
a := 0 ;
for k from 1 to (n-2)/2 do
a := a+procname(n-2*k-1, l-k)*binomial(n-k-2, k) ;
end do:
a ;
end if;
end proc:
A201693 := proc(nmax)
g := 1-t ;
for n from 2 to nmax do
for l from 0 to n/2 do
g := g-c(n, l)*t^n*(-1)^l/n! ;
end do:
end do:
taylor(1/g, t=0, nmax) ;
end proc:
nmax := 25 ;
egf := A201693(nmax) ;
for n from 0 to nmax-1 do
printf("%d, ", coeftayl(egf, t=0, n)*n!) ;
end do: # R. J. Mathar, Dec 04 2011
# second Maple program:
b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1, `if`(0<t and j<t, -j, 0)), j=1..u)+
add(b(u+j-1, o-j, j), j=`if`(t<0, -t, 1)..o))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..25); # Alois P. Heinz, Nov 07 2013
MATHEMATICA
b[u_, o_, t_] := b[u, o, t] = If[u+o == 0, 1, Sum[b[u-j, o+j-1, If[0<t && j<t, -j, 0]], {j, 1, u}] + Sum[b[u+j-1, o-j, j], {j, If[t<0, -t, 1], o}]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 18 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 03 2011
EXTENSIONS
Definition corrected by N. J. A. Sloane, Mar 15 2015
STATUS
approved