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 A236408 Number of increasing planar st-graphs with n edges. 0
 1, 1, 3, 9, 33, 131, 561, 2535, 11971, 58579, 295297, 1526427, 8061879, 43380351, 237266225, 1316536991, 7399318871, 42065753191, 241628448517, 1400957386207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS From Michael Wallner, Aug 17 2020: (Start) A graph with m vertices is called increasing, or topolicically ordered, if each vertex v is assigned a number l(v) from {1,...,m} and if there is a directed path from vertex v to vertex w then l(v) < l(w). Note that a planar st-graph is an actual embedding into the plane, i.e., we distinguish a left-to-right order on the children of each node. In other words, it is a plane graph, a concept also sometimes called isotopy. (End) REFERENCES Ioannis G. Tollis, Giuseppe Di Battista, Peter Eades and Roberto Tamassia, Graph drawing, Prentice Hall Inc., Upper Saddle River, NJ, 1999. Algorithms for the visualization of graphs. MR2064104 (2005i:68067). See Sect. 4.2. LINKS Alin Bostan, Jordan Tirrell, Bruce W. Westbury, and Yi Zhang, On sequences associated to the invariant theory of rank two simple Lie algebras, arXiv:1911.10288 [math.CO], 2019. James Cranch, Representing and Enumerating Two-Dimensional Pasting Diagrams, 2014. FORMULA Conjecture: (n+2)*(n+3)*a(n) = 2*n*(2*n+1)*a(n-1) + (n-2)*(19*n-9)*a(n-2) + 14*(n-3)*(n-2)*a(n-3). - Vaclav Kotesovec, Feb 14 2014 EXAMPLE From Michael Wallner, Aug 17 2020: (Start) All edges are directed to the bottom. a(3)=3:    1       1           1    |       |\         /|    2       | 2       2 |    |       |/         \|    3       3           3    |    4 a(4)=9:    1    1       1     1       1     1       1      1        1    |    |       |     |\     /|     |\     /|     / \      / \    2    2       2     2 |   | 2     2 |   | 2    2   3    3   2    |    |\     /|     |/     \|     | |   | |     \ /      \ /    3    3 |   | 3     3       3     3 |   | 3      4        4    |    |/     \|     |       |     |/     \|    4    4       4     4       4     4       4    |    5 (End) CROSSREFS Sequence in context: A151043 A151044 A247195 * A217617 A320181 A238113 Adjacent sequences:  A236405 A236406 A236407 * A236409 A236410 A236411 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Feb 03 2014 EXTENSIONS Name clarified by Michael Wallner, Aug 17 2020 STATUS approved

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Last modified June 21 23:35 EDT 2021. Contains 345367 sequences. (Running on oeis4.)