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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 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

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