

A240020


Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(2n1).


4



1, 2, 2, 3, 3, 4, 4, 5, 3, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 5, 5, 11, 12, 12, 13, 5, 13, 14, 6, 6, 14, 15, 15, 16, 16, 17, 7, 7, 17, 18, 12, 18, 19, 19, 20, 8, 8, 20, 21, 21, 22, 22, 23, 32, 23, 24, 24, 25, 7, 25, 26, 10, 10, 26, 27, 27, 28, 8, 8, 28, 29, 11, 11, 29, 30, 30, 31, 31, 32, 12, 26, 12, 32, 33, 9, 9, 33, 34, 34
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OFFSET

1,2


COMMENTS

Row n lists the parts of the symmetric representation of A008438(n1).
Also these are the parts from the oddindexed rows of A237270.
Also these are the parts in the quadrants 1 and 3 of the spiral described in A239660, see example.
Row sums give A008438.
The length of row n is A237271(2n1).
Both column 1 and the right border are equal to n.
Note that also the sequence can be represented in a quadrant.
We can find the spiral (mentioned above) on the terraces of the stepped pyramid described in A244050.  Omar E. Pol, Dec 07 2016


LINKS

Table of n, a(n) for n=1..92.


EXAMPLE

1;
2, 2;
3, 3;
4, 4;
5, 3, 5;
6, 6;
7, 7;
8, 8, 8;
9, 9;
10, 10;
11, 5, 5, 11;
12, 12;
13, 5, 13;
14, 6, 6, 14;
15, 15;
16, 16;
17, 7, 7, 17;
18, 12, 18;
19, 19;
20, 8, 8, 20;
21, 21;
22, 22;
23, 32, 23;
24, 24;
25, 7, 25;
...
Illustration of initial terms (rows 1..8):
.
. _ _ _ _ _ _ _ 7
. _ _ _ _ _ _ _
. 
. _ _
. _ _ _ _ _ 5 _
. _ _ _ _ _ 
. _ _ 3 _ _ _ 7
. _   
. _ _ _ 3 __ _ 5  
. _ _ _    
. _ _ 3    
.      
. _ 1      
. _ _ _ _ _ _ _ _
.        
.       __ _
.       2 _ _
.     __ 2
.     4 _
.   __ _ _ _ _ _
.   6 _ _ _ _ _
. __ _ _ _ 4
. 8  _ _ 
. _  _ _ _ _ _ _
. _ _ _ _ _ _ _ _
. 8 _ _ 6
. 
. _ _ _ _ _ _ _ _
. _ _ _ _ _ _ _ _
. 8
.
The figure shows the quadrants 1 and 3 of the spiral described in A239660.
For n = 5 we have that 2*5  1 = 9 and the 9th row of A237593 is [5, 2, 2, 2, 2, 5] and the 8th row of A237593 is [5, 2, 1, 1, 2, 5] therefore between both symmetric Dyck paths there are three regions (or parts) of sizes [5, 3, 5], so row 5 is [5, 3, 5], see the third arm of the spiral in the first quadrant.
The sum of divisors of 9 is 1 + 3 + 9 = A000203(9) = 13. On the other hand the sum of the parts of the symmetric representation of sigma(9) is 5 + 3 + 5 = 13, equaling the sum of divisors of 9.


CROSSREFS

Cf. A000203, A005408, A008438, A112610, A196020, A236104, A237048, A237270, A237271, A237591, A237593, A239053, A239660, A239931, A239933, A244050, A245092, A262626.
Sequence in context: A220032 A219773 A187446 * A336430 A167232 A319468
Adjacent sequences: A240017 A240018 A240019 * A240021 A240022 A240023


KEYWORD

nonn,tabf


AUTHOR

Omar E. Pol, Mar 31 2014


STATUS

approved



