OFFSET
1,2
COMMENTS
For more information about the mentioned Dyck paths see A237593.
EXAMPLE
n Triangle begins:
1 1;
2 2, 3;
3 4, 5;
4 0;
5 6, 7;
6 8,
7 9, 10, 11;
8 0;
9 12, 13, 14;
10 0;
11 15;
12 16, 17;
13 18, 19;
14 0;
15 20, 21, 22, 23;
16 0;
...
MATHEMATICA
(* last computed value is dropped to avoid a potential under count of crossings *)
a240542[n_] := Sum[(-1)^(k+1)Ceiling[(n+1)/k-(k+1)/2], {k, 1, Floor[-1/2+1/2 Sqrt[8n+1]]}]
pathGroups[n_] := Module[{t}, t=Table[{}, a240542[n]]; Map[AppendTo[t[[a240542[#]]], #]&, Range[n]]; Map[If[t[[#]]=={}, t[[#]]={0}]&, Range[Length[t]]]; Most[t]]
a279385[n_] := Flatten[pathGroups[n]]
a279385[70] (* sequence *)
a279385T[n_] := TableForm[pathGroups[n], TableHeadings->{Range[a240542[n]-1], None}]
a279385T[24] (* display of irregular triangle - Hartmut F. W. Hoft, Feb 02 2022 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 12 2016
EXTENSIONS
More terms from Omar E. Pol, Jun 20 2018
STATUS
approved