

A317303


Numbers k such that both Dyck paths of the symmetric representation of sigma(k) have a central peak.


6



2, 7, 8, 9, 16, 17, 18, 19, 20, 29, 30, 31, 32, 33, 34, 35, 46, 47, 48, 49, 50, 51, 52, 53, 54, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 154, 155, 156, 157, 158, 159, 160
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OFFSET

1,1


COMMENTS

Also triangle read by rows which gives the oddindexed rows of triangle A014132.
There are no triangular number (A000217) in this sequence.
For more information about the symmetric representation of sigma see A237593 and its related sequences.
Equivalently, numbers k with the property that both Dyck paths of the symmetric representation of sigma(k) have an odd number of peaks.  Omar E. Pol, Sep 13 2018


LINKS



EXAMPLE

Written as an irregular triangle in which the row lengths are the odd numbers, the sequence begins:
2;
7, 8, 9;
16, 17, 18, 19, 20;
29, 30, 31, 32, 33, 34, 35;
46, 47, 48, 49, 50, 51, 52, 53, 54;
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77;
92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104;
121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135;
...
Illustration of initial terms:

k sigma(k) Diagram of the symmetry of sigma

_ _ _ _ _ _ _ _ _
_           
2 3 _ _          
         
__        
_ _ __      
_ _ _ _ _       
7 8 _ _ _ _ _ _      
8 15 _ _ _ _ _ _ _ _     
9 13 _ _ _ _ _  _ _ __   
_  _ _ __ 
_ _  _ _ _ _
_ _ _ _ _ 
 _ _ _ _
   
_ _ _ _ _ _ _ _  _ _ _ _
16 31 _ _ _ _ _ _ _ _ _  _ _
17 18 _ _ _ _ _ _ _ _ _  
18 39 _ _ _ _ _ _ _ _ _ _ 
19 20 _ _ _ _ _ _ _ _ _ _ 
20 42 _ _ _ _ _ _ _ _ _ _ _
.
For the first nine terms of the sequence we can see in the above diagram that both Dyck path (the smallest and the largest) of the symmetric representation of sigma(k) have a central peak.


CROSSREFS

Row sums give the oddindexed terms of A006002.
Right border gives the positive terms of A014107, also the oddindexed terms of A000096.
Cf. A000203, A005408, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A237271, A239660, A239931, A239932, A239933, A239934, A244050, A245092, A249351, A262626.


KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



