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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.
LINKS
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
KEYWORD
nonn,more
AUTHOR
David E Speyer (speyer(AT)post.harvard.edu), Jul 02 2007
STATUS
approved

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Last modified July 24 02:45 EDT 2024. Contains 374575 sequences. (Running on oeis4.)