1,2

It is easy to mistake these for monotone triangles.

a(3)=7 because the vertices of GT(3) are

123

12

1

---

123

12

2

---

123

13

1

---

123

13

3

---

123

23

2

---

123

23

3

---

123

22

2

---

(* G computes the required sequence, F computes the similar sequence with any monotone sequence permitted as the input top row. Note that F and Bifurcate cache their values. *) Bifurcate[l_] := Bifurcate[l] = If[Length[l] == 1, { {} }, Union[Map[Prepend[ #, l[[1]]] &, Bifurcate[Drop[l, 1]]], Map[ Prepend[ #, l[[2]]] &, Bifurcate[Drop[l, 1]]]]] F[l_] := F[l] = If[Length[l] == 0, 1, Apply[Plus, Map[F, Bifurcate[l]]]] G[n_] := F[Range[n]]

Sequence in context: A008608 A028441 A006455 this_sequence A106871 A107376 A087804

Adjacent sequences: A130712 A130713 A130714 this_sequence A130716 A130717 A130718

nonn

David E Speyer (speyer(AT)post.harvard.edu), Jul 02 2007