A130715 Number of vertices of the Gelfand Tsetlin-polytope. Alternatively, the number of Gelfand-Tsetlin patterns with top row 1234...n and such that every entry in a given row also appears in the row above it.

1, 2, 7, 40, 358, 4884, 99665, 3000736, 131932016, 8403206128

Offset

1,2

Comments

It is easy to mistake these for monotone triangles.

Links

Table of n, a(n) for n=1..10.

Luca De Feo, David Jao and Jerome Plut, Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies, Cryptology ePrint Archive: Report 2011/506. - From N. J. A. Sloane, Dec 22 2012

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

Sequence in context: A008608 A028441 A006455 * A317723 A340005 A325061

Adjacent sequences: A130712 A130713 A130714 * A130716 A130717 A130718

Keyword

nonn,more

Author

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

Status

approved