OFFSET
1,6
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
Conjectures from Chai Wah Wu, Apr 15 2024: (Start)
a(n) = 5*a(n-1) - 7*a(n-2) - a(n-3) + 8*a(n-4) - 4*a(n-5) for n > 7.
G.f.: x^5*(x^2 - x + 1)/((x - 1)^2*(x + 1)*(2*x - 1)^2). (End)
EXAMPLE
The a(5) = 1 through a(7) = 14 trees:
((o)(o)) ((o)(oo)) ((o)(ooo))
(o(o)(o)) ((oo)(oo))
(((o)(o))) (o(o)(oo))
((o)((o))) (oo(o)(o))
(((o))(oo))
(((o)(oo)))
((o)((oo)))
((o)(o(o)))
((o(o)(o)))
(o((o)(o)))
(o(o)((o)))
((((o)(o))))
(((o)((o))))
((o)(((o))))
MATHEMATICA
art[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[art/@c], OrderedQ], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[art[n], Count[#, _[__], {0, Infinity}]==Depth[#]-1&]], {n, 1, 10}]
PROG
(PARI) \\ Needs R(n, f) defined in A358589.
seq(n) = {Vec(R(n, (h, p)->polcoef(subst(p, x, x/y), -h, y)), -n)} \\ Andrew Howroyd, Jan 01 2023
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 23 2022
EXTENSIONS
Terms a(19) and beyond from Andrew Howroyd, Jan 01 2023
STATUS
approved