The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A303730 Number of noncrossing path sets on n nodes with each path having at least two nodes. 4
 1, 0, 1, 3, 10, 35, 128, 483, 1866, 7344, 29342, 118701, 485249, 2001467, 8319019, 34810084, 146519286, 619939204, 2635257950, 11248889770, 48198305528, 207222648334, 893704746508, 3865335575201, 16761606193951, 72860178774410, 317418310631983, 1385703968792040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Paths are constructed using noncrossing line segments between the vertices of a regular n-gon. Isolated vertices are not allowed. A noncrossing path set is a noncrossing forest (A054727) where each tree is restricted to being a path. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 Isaac DeJager, Madeleine Naquin, Frank Seidl, Colored Motzkin Paths of Higher Order, VERUM 2019. FORMULA G.f.: G(x)/x where G(x) is the reversion of x*(1 - 2*x)^2/(1 - 4*x + 5*x^2 - x^3). EXAMPLE Case n=3: There are 3 possibilities: .      o       o       o     /         \     / \    o---o   o---o   o   o . Case n=4: There are 10 possibilities: .    o   o   o   o   o---o   o---o   o---o    |   |   |   |   |       |   |       |    o   o   o---o   o---o   o   o   o---o .    o---o   o---o   o---o   o   o   o   o              /       \     | / |   | \ |    o---o   o---o   o---o   o   o   o   o . MATHEMATICA InverseSeries[x*(1 - 2*x)^2/(1 - 4*x + 5*x^2 - x^3) + O[x]^30, x] // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Jul 03 2018, from PARI *) PROG (PARI) Vec(serreverse(x*(1 - 2*x)^2/(1 - 4*x + 5*x^2 - x^3) + O(x^30))) CROSSREFS Cf. A054727, A303729. Sequence in context: A078789 A299443 A128736 * A149037 A228769 A296164 Adjacent sequences:  A303727 A303728 A303729 * A303731 A303732 A303733 KEYWORD nonn AUTHOR Andrew Howroyd, Apr 29 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 7 00:22 EDT 2021. Contains 343609 sequences. (Running on oeis4.)