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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. 0
1, 2, 7, 40, 358, 4884, 99665, 3000736, 131932016, 8403206128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It is easy to mistake these for monotone triangles.

REFERENCES

Luca De Feo, David Jao and Jerome Plut, Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies, http://www.prism.uvsq.fr/~dfl/fichiers/pq-long.pdf. - From N. J. A. Sloane, Dec 22 2012

LINKS

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

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 A325061 A215207

Adjacent sequences:  A130712 A130713 A130714 * A130716 A130717 A130718

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)