Metadata
bibkey: barker2019a326244
authors: Colin Barker
year: 2019
title: "OEIS A326244, Number of labeled n-vertex simple graphs without crossing or nesting edges"
doi: null
url: https://oeis.org/A326244
claim: "Number of labeled n-vertex simple graphs without crossing or nesting edges. Two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b, and nesting if a < c < d < b or c < a < b < d. Conjectures from _Colin Barker_, Jun 28 2019: (Start) G.f.: (1 - x)*(1 - 4*x) / (1 - 6*x + 8*x^2 - 4*x^3). a(n) = 6*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>2. (End) Entry: _Gus Wiseman_, Jun 20 2019."
strata_touched:
- D5/S1/Words/Patterns/NoncrossingNonnestingGraphRecurrence
license: citation-only
triage: anchor
OEIS A326244
The NAME, COMMENTS, and FORMULA fields define the counted labeled graphs and state Colin Barker’s 2019 recurrence conjecture. The entry is authored by Gus Wiseman; the conjecture is attributed in the entry to Colin Barker.
Verified locator
- URL: https://oeis.org/A326244
- Locator: NAME, COMMENTS, and FORMULA; Colin Barker, Jun 28 2019; entry author Gus Wiseman, Jun 20 2019.
The FORMULA conjecture line is:
a(n) = 6a(n-1) - 8a(n-2) + 4*a(n-3) for n>2.