

A130715


Number of vertices of the Gelfand Tsetlinpolytope. Alternatively, the number of GelfandTsetlin patterns with top row 1234...n and such that every entry in a given row also appears in the row above it.


0




OFFSET

1,2


COMMENTS

It is easy to mistake these for monotone triangles.


LINKS



EXAMPLE

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



MATHEMATICA

(* 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]]


CROSSREFS



KEYWORD

nonn,more


AUTHOR

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


STATUS

approved



