|
|
A279385
|
|
Irregular triangle read by rows in which row n lists the numbers k such that the largest Dyck path of the symmetric representation of sigma(k) contains the point (n,n), or row n is 0 if no such k exists.
|
|
8
|
|
|
1, 2, 3, 4, 5, 0, 6, 7, 8, 9, 10, 11, 0, 12, 13, 14, 0, 15, 16, 17, 18, 19, 0, 20, 21, 22, 23, 0, 24, 25, 26, 27, 0, 28, 29, 0, 30, 31, 32, 33, 34, 0, 35, 36, 37, 38, 39, 0, 40, 41, 0, 42, 43, 44, 0, 45, 46, 47, 0, 48, 49, 50, 51, 52, 53, 0, 54, 55, 0, 56, 57, 58, 59, 0, 60, 61, 62, 0, 63, 64, 65, 0, 66, 67, 68, 69, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
For more information about the mentioned Dyck paths see A237593.
|
|
LINKS
|
|
|
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}]
|
|
CROSSREFS
|
Cf. A259179(n) is the number of positive terms in row n.
Cf. A000203, A196020, A236104, A235791, A237048, A237591, A237593, A240542, A244050, A245092, A259179, A262626, A279286.
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|