OFFSET
0,2
COMMENTS
The additional terms were found using dynamic programming to count the maximal chains in the distributive lattice of order-preserving functions from the chain of length n to J(P), where J is the lattice of downsets of the poset P = 2x2. - Nick Krempel, Jul 08 2010
REFERENCES
Stanley, R., Enumerative Combinatorics, Vol. 2, Prop. 7.10.3 and Vol. 1, Sec 3.5, Chains in Distributive Lattices.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..180 (first 41 terms from Nick Krempel)
MAPLE
b:= proc(x, y, u, w) option remember;
`if`(x=0 and y=0 and u=0 and w=0, 1, `if`(x>y and x>u,
b(x-1, y, u, w), 0)+ `if`(y>w, b(x, y-1, u, w), 0)+
`if`(u>w, b(x, y, u-1, w), 0)+ `if`(w>0, b(x, y, u, w-1), 0))
end:
a:= n-> b(n$4):
seq(a(n), n=0..20); # Alois P. Heinz, Apr 27 2012
MATHEMATICA
b[x_, y_, u_, w_] := b[x, y, u, w] = If[x == 0 && y == 0 && u == 0 && w == 0, 1, If[x>y && x>u, b[x-1, y, u, w], 0] + If[y>w, b[x, y-1, u, w], 0] + If[u>w, b[x, y, u-1, w], 0] + If[w>0, b[x, y, u, w-1], 0]]; a[n_] := b[n, n, n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 29 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Mitch Harris, Dec 27 2005
EXTENSIONS
More terms from Nick Krempel, Jul 08 2010
STATUS
approved