OFFSET
1,3
COMMENTS
Consider the ranked poset L(n) of partitions defined in A002846. Add additional edges from each partition to any other partition that is a refinement of it. In L(5), for example, we add edges from 5^1 to 31^2, 2^21, 21^3 and 1^5, from 41 to 21^3 and 1^5, and so on.
Then a(n) is the total number of paths in the augmented poset of any length from n^1 to 1^n.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..40
Olivier Gérard, The ranked posets L(2),...,L(8)
MAPLE
b:= proc(l) option remember; local i, j, n, t; n:=nops(l);
`if`(n<2, {[0]}, `if`(l[-1]=0, b(subsop(n=NULL, l)), {l,
seq(`if`(l[i]=0, {}[], {seq(b([seq(l[t]-`if`(t=1, l[t],
`if`(t=i, 1, `if`(t=j and t=i-j, -2, `if`(t=j or t=i-j,
-1, 0)))), t=1..n)])[], j=1..i/2)}[]), i=2..n)}))
end:
p:= proc(l) option remember;
`if`(nops(l)=1, 1, add(p(x), x=b(l) minus {l}))
end:
a:= n-> p([0$(n-1), 1]):
seq(a(n), n=1..25); # Alois P. Heinz, Jun 12 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 11 2012
EXTENSIONS
More terms from Alois P. Heinz, Jun 11 2012
Edited by Alois P. Heinz at the suggestion of Gus Wiseman, May 02 2016
STATUS
approved