OFFSET
1,1
COMMENTS
Row n is a palindromic composition of sigma(4n-2).
Row n is also the row 4n-2 of A237270.
Row n has length A237271(4n-2).
Row sums give A239052.
Also row n lists the parts of the symmetric representation of sigma in the n-th arm of the second quadrant of the spiral described in A239660, see example.
For the parts of the symmetric representation of sigma(4n-3), see A239931.
For the parts of the symmetric representation of sigma(4n-1), see A239933.
For the parts of the symmetric representation of sigma(4n), see A239934.
We can find the spiral (mentioned above) on the terraces of the pyramid described in A244050. - Omar E. Pol, Dec 06 2016
EXAMPLE
The irregular triangle begins:
3;
12;
9, 9;
12, 12;
39;
18, 18;
21, 21;
72;
27, 27;
30, 30;
96;
36, 36;
39, 15, 39;
120;
45, 45;
48, 48;
...
Illustration of initial terms in the second quadrant of the spiral described in A239660:
. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
. | _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
. | |
. | |
. | | _ _ _ _ _ _ _ _ _ _ _ _ _ _
. _ _ _| | | _ _ _ _ _ _ _ _ _ _ _ _ _|
. | | | |
. _ _| _ _ _| | |
. 72 _| | | | _ _ _ _ _ _ _ _ _ _ _ _
. _| _| 21 _ _| | | _ _ _ _ _ _ _ _ _ _ _|
. | _| |_ _ _| | |
. _ _| _| _ _| | |
. | _ _| _| 18 _ _| | _ _ _ _ _ _ _ _ _ _
. | | | |_ _ _| | _ _ _ _ _ _ _ _ _|
. _ _ _ _ _| | 21 _ _| _| | |
. | _ _ _ _ _ _| | | _| _ _| |
. | | _ _ _ _ _| | 18 _ _| | | _ _ _ _ _ _ _ _
. | | | _ _ _ _ _| | | 39 _| _ _| | _ _ _ _ _ _ _|
. | | | | _ _ _ _| | _ _| _| | |
. | | | | | _ _ _ _| | _| 12 _| |
. | | | | | | _ _ _| | |_ _| _ _ _ _ _ _
. | | | | | | | _ _ _ _| 12 _ _| | _ _ _ _ _|
. | | | | | | | | _ _ _| | 9 _| |
. | | | | | | | | | _ _ _| 9 _|_ _|
. | | | | | | | | | | _ _| | _ _ _ _
. | | | | | | | | | | | _ _| 12 _| _ _ _|
. | | | | | | | | | | | | _| |
. | | | | | | | | | | | | | _ _|
. | | | | | | | | | | | | | | 3 _ _
. | | | | | | | | | | | | | | | _|
. |_| |_| |_| |_| |_| |_| |_| |_|
.
For n = 7 we have that 4*7-2 = 26 and the 26th row of A237593 is [14, 5, 2, 2, 2, 1, 1, 2, 2, 2, 5, 14] and the 25th row of A237593 is [13, 5, 3, 1, 2, 1, 1, 2, 1, 3, 5, 13] therefore between both Dyck paths there are two regions (or parts) of sizes [21, 21], so row 7 is [21, 21].
The sum of divisors of 26 is 1 + 2 + 13 + 26 = A000203(26) = 42. On the other hand the sum of the parts of the symmetric representation of sigma(26) is 21 + 21 = 42, equaling the sum of divisors of 26.
CROSSREFS
KEYWORD
nonn,tabf,more
AUTHOR
Omar E. Pol, Mar 29 2014
STATUS
approved