A130715 - OEIS

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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.

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

	OFFSET	`1,2`
	COMMENTS	`It is easy to mistake these for monotone triangles.`
	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 * A106871 A107376 A087804` `Adjacent sequences: A130712 A130713 A130714 * A130716 A130717 A130718`
	KEYWORD	`nonn`
	AUTHOR	`David E Speyer (speyer(AT)post.harvard.edu), Jul 02 2007`

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Last modified February 17 23:32 EST 2012. Contains 206085 sequences.