A221529 -id:A221529 - cp's OEIS frontend

A346562 Irregular triangle read by rows in which row n lists the first n - 2 terms of A000005 together with the sum of A000005(n-1) and A000005(n), with a(1) = 1.

1, 3, 1, 4, 1, 2, 5, 1, 2, 2, 5, 1, 2, 2, 3, 6, 1, 2, 2, 3, 2, 6, 1, 2, 2, 3, 2, 4, 6, 1, 2, 2, 3, 2, 4, 2, 7, 1, 2, 2, 3, 2, 4, 2, 4, 7, 1, 2, 2, 3, 2, 4, 2, 4, 3, 6, 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 8, 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 8, 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 6

Offset: 1

Omar E. Pol, Jul 23 2021

T(n,k) is the total number of divisors related to the terraces that are in the k-th level that contains terraces starting from the base of the symmetric tower described in A221529.

			Triangle begins:
1;
3;
1, 4;
1, 2, 5;
1, 2, 2, 5;
1, 2, 2, 3, 6;
1, 2, 2, 3, 2, 6;
1, 2, 2, 3, 2, 4, 6;
1, 2, 2, 3, 2, 4, 2, 7;
1, 2, 2, 3, 2, 4, 2, 4, 7;
1, 2, 2, 3, 2, 4, 2, 4, 3, 6;
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 8;
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 8;
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 6;
...

The length of row n is A028310(n-1).
Row sums give A006218, n >= 1.
Leading diagonal gives A092405.
Other diagonals give A000005.
Column 1 gives the absolute values of A260196.
Companion of A346533.
Cf. A221529, A237270, A237593, A336811, A338156, A340035.

A350333 Irregular triangle read by rows in which row n lists all elements of the arrangement of the correspondence divisor/part related to the partitions of n in the following order: row n lists the n-th row of A026792 followed by the n-th row of A338156.

Original entry on oeis.org

1, 1, 2, 1, 1, 1, 2, 1, 3, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 4, 2, 2, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 3, 1, 2, 1, 2, 1, 1, 1, 5, 3, 2, 4, 1, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 2, 4, 1, 3, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 6, 3, 3, 4, 2, 2, 2, 2, 5, 1

Offset: 1

Omar E. Pol, Dec 25 2021

			Triangle begins:
[1], [1];
[2, 1, 1], [1, 2, 1];
[3, 2, 1, 1, 1, 1], [1, 3, 1, 2, 1, 1];
[4, 2, 2, 3, 1, 2, 1, 1, 1, 1, 1, 1], [1, 2, 4, 1, 3, 1, 2, 1, 2, 1, 1, 1];
...
Illustration of the first six rows of triangle in an infinite table:
.
|---|---------|-----|-------|---------|-----------|-------------|---------------|
| n |         |  1  |   2   |    3    |     4     |      5      |       6       |
|---|---------|-----|-------|---------|-----------|-------------|---------------|
|   |         |     |       |         |           |             |  6            |
| P |         |     |       |         |           |             |  3 3          |
| A |         |     |       |         |           |             |  4 2          |
| R |         |     |       |         |           |             |  2 2 2        |
| T |         |     |       |         |           |  5          |  5 1          |
| I |         |     |       |         |           |  3 2        |  3 2 1        |
| T |         |     |       |         |  4        |  4 1        |  4 1 1        |
| I |         |     |       |         |  2 2      |  2 2 1      |  2 2 1 1      |
| O |         |     |       |  3      |  3 1      |  3 1 1      |  3 1 1 1      |
| N |         |     |  2    |  2 1    |  2 1 1    |  2 1 1 1    |  2 1 1 1 1    |
| S |         |  1  |  1 1  |  1 1 1  |  1 1 1 1  |  1 1 1 1 1  |  1 1 1 1 1 1  |
----|---------|-----|-------|---------|-----------|-------------|---------------|
|   | A027750 |  1  |  1 2  |  1   3  |  1 2   4  |  1       5  |  1 2 3     6  |
|   | A027750 |     |  1    |  1 2    |  1   3    |  1 2   4    |  1       5    |
|   | A027750 |     |       |  1      |  1 2      |  1   3      |  1 2   4      |
|   | A027750 |     |       |  1      |  1 2      |  1   3      |  1 2   4      |
|   | A027750 |     |       |         |  1        |  1 2        |  1   3        |
| D | A027750 |     |       |         |  1        |  1 2        |  1   3        |
| I | A027750 |     |       |         |  1        |  1 2        |  1   3        |
| V | A027750 |     |       |         |           |  1          |  1 2          |
| I | A027750 |     |       |         |           |  1          |  1 2          |
| S | A027750 |     |       |         |           |  1          |  1 2          |
| O | A027750 |     |       |         |           |  1          |  1 2          |
| R | A027750 |     |       |         |           |  1          |  1 2          |
| S | A027750 |     |       |         |           |             |  1            |
|   | A027750 |     |       |         |           |             |  1            |
|   | A027750 |     |       |         |           |             |  1            |
|   | A027750 |     |       |         |           |             |  1            |
|   | A027750 |     |       |         |           |             |  1            |
|   | A027750 |     |       |         |           |             |  1            |
|   | A027750 |     |       |         |           |             |  1            |
|---|---------|-----|-------|---------|-----------|-------------|---------------|
.
For n = 6 in the upper zone of the above table we can see the partitions of 6 in reverse-colexicographic order in accordance with the 6th row of A026792.
In the lower zone of the table we can see the terms from the 6th row of A338156, these are the divisors of the numbers from the 6th row of A176206.
Note that in the lower zone of the table every row gives A027750.
The total number of rows in the table is equal to A000070(6+1) = 30.
The remarkable fact is that the elements in the lower zone of the arrangement are the same as the elements in the upper zone but in other order.
For an explanation of the connection of the elements of the upper zone with the elements of the lower zone, that is the correspondence divisor/part, see A338156.
For n = 10 we can see a representation of the upper zone (the partitions) and of the lower zone (the divisors) with the two polycubes described in A221529 respectively: a prism of partitions and a tower whose terraces are the symmetric representation of sigma(m), for m = 1..10. Each polycube has A066186(10) = 420 cubic cells, hence the total number of cubic cells is equal to A220909(10) = 840, equaling the sum of the 10th row of this triangle.

Row sums give A220909.
Row lengths give A211978.
Cf. A350357 (analog for the last section of the set of partitions of n).
Cf. A000041, A000070, A006128, A026792, A027750, A066186, A135010, A176206, A221529, A237593, A336811, A336812, A338156, A340035.

A350357 Irregular triangle read by rows in which row n lists all elements of the arrangement of the correspondence divisor/part related to the last section of the set of partitions of n in the following order: row n lists the n-th row of A138121 followed by the n-th row of A336812.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 3, 1, 4, 2, 2, 1, 1, 1, 1, 2, 4, 1, 2, 1, 5, 3, 2, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 2, 1, 1, 6, 3, 3, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 6, 1, 2, 4, 1, 3, 1, 2, 1, 2, 1, 1, 7, 4, 3, 5, 2, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Omar E. Pol, Dec 26 2021

			Triangle begins:
[1], [1];
[2, 1], [1, 2];
[3, 1, 1], [1, 3, 1];
[4, 2, 2, 1, 1, 1], [1, 2, 4, 1, 2, 1];
[5, 3, 2, 1, 1, 1, 1, 1], [1, 5, 1, 3, 1, 2, 1, 1];
...
Illustration of the first six rows of triangle in an infinite table:
|---|---------|-----|-------|---------|-----------|-------------|---------------|
| n |         |  1  |   2   |    3    |     4     |      5      |       6       |
|---|---------|-----|-------|---------|-----------|-------------|---------------|
|   |         |     |       |         |           |             |  6            |
|   |         |     |       |         |           |             |  3 3          |
|   |         |     |       |         |           |             |  4 2          |
| P |         |     |       |         |           |             |  2 2 2        |
| A |         |     |       |         |           |  5          |    1          |
| R |         |     |       |         |           |  3 2        |      1        |
| T |         |     |       |         |  4        |    1        |      1        |
| S |         |     |       |         |  2 2      |      1      |        1      |
|   |         |     |       |  3      |    1      |      1      |        1      |
|   |         |     |  2    |    1    |      1    |        1    |          1    |
|   |         |  1  |    1  |      1  |        1  |          1  |            1  |
|---|---------|-----|-------|---------|-----------|-------------|---------------|
| D | A027750 |  1  |  1 2  |  1   3  |  1 2   4  |  1       5  |  1 2 3     6  |
| I | A027750 |     |       |  1      |  1 2      |  1   3      |  1 2   4      |
| V | A027750 |     |       |         |  1        |  1 2        |  1   3        |
| I | A027750 |     |       |         |           |  1          |  1 2          |
| S | A027750 |     |       |         |           |  1          |  1 2          |
| O | A027750 |     |       |         |           |             |  1            |
| R | A027750 |     |       |         |           |             |  1            |
| S |         |     |       |         |           |             |               |
|---|---------|-----|-------|---------|-----------|-------------|---------------|
.
For n = 6 in the upper zone of the above table we can see the parts of the last section of the set of partitions of 6 in reverse-colexicographic order in accordance with the 6th row of A138121.
In the lower zone of the table we can see the terms from the 6th row of A336812, these are the divisors of the numbers from the 6th row of A336811.
Note that in the lower zone of the table every row gives A027750.
The remarkable fact is that the elements in the lower zone of the arrangement are the same as the elements in the upper zone but in other order.
For an explanation of the connection of the elements of the upper zone with the elements of the lower zone, that is the correspondence divisor/part, see A336812 and A338156.
The growth of the upper zone of the table is in accordance with the growth of the modular prism described in A221529.
The growth of the lower zone of the table is in accordance with the growth of the tower described also in A221529.
The number of cubic cells added at n-th stage in each polycube is equal to A138879(10) = 150, hence the total number of cubic cells added at n-th stage is equal to 2*A138879(10) = 300, equaling the sum of the 10th row of this triangle.

Companion of A350333.
Row sums give 2*A138879.
Row lengths give 2*A138137.
Cf. A002865, A135010, A138121, A138879, A221529, A237593, A336812, A339278.

A384230 Number of subparts in the central part of the symmetric representation of sigma(n).

Original entry on oeis.org

1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 0, 2, 1, 0, 3, 0, 2, 0, 0, 0, 2, 1, 0, 0, 2, 0, 4, 0, 1, 0, 0, 2, 3, 0, 0, 0, 2, 0, 4, 0, 0, 4, 0, 0, 2, 1, 1, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 2, 1, 0, 4, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 4, 0, 0, 0

Offset: 1

Omar E. Pol, Jun 29 2025

This sequence shares infinitely many terms with A067742 from which first differs at a(18). It also shares with A067742 the positions of zeros and nonzeros.
Observation: consider the 2-dense sublists of divisors of n. At least for the first 88 terms a(n) coincides with the number of odd terms in the central 2-dense sublist of divisors of n. For more information see A384225 and A280940.
See the "Discussion" text file in the first link for more comments.

			See the "Discussion" text file in the first link for the examples.

Omar E. Pol, Discussion of the Sequence A384230.
Omar E. Pol, Illustration of initial terms of A000203 in the pyramid.
Omar E. Pol, Illustration of initial terms of A001065 in the pyramid.
Omar E. Pol, Illustration of initial terms of A048050 in the pyramid.
Omar E. Pol, Illustration of initial terms of A067742 in the pyramid.
Omar E. Pol, Illustration of initial terms of A224613 (black spiders).
Omar E. Pol, Illustration of initial terms of A237593 (essentially a template for the Pop-Up pyramid).
Omar E. Pol, Prism of partitions of 10 and its companion tower (both have the same volume).
Omar E. Pol, The symmetric representation of sigma(n), n = 1..64 (the top view of the pyramid and of the tower).

Cf. A001227 (number of subparts), A071561 (positions of zeros), A071562 (positions of nonzeros), A237270 (parts), A237271, A237593, A279387 (subparts), A280940, A384225, A335574, A338488, A377654.

See the "Discussion" text file in the first link for more cross-references.

a(n) = 0 if and only if A067742(n) = 0.
a(n) >= A067742(n).
(a(n) - A067742(n)) is an even number.

Edited by Omar E. Pol, Aug 24 2025

A350637 Triangle read by rows: T(n,k) in which row n lists the first n terms of A024916 in reverse order, 1 <= k <= n.

Original entry on oeis.org

1, 4, 1, 8, 4, 1, 15, 8, 4, 1, 21, 15, 8, 4, 1, 33, 21, 15, 8, 4, 1, 41, 33, 21, 15, 8, 4, 1, 56, 41, 33, 21, 15, 8, 4, 1, 69, 56, 41, 33, 21, 15, 8, 4, 1, 87, 69, 56, 41, 33, 21, 15, 8, 4, 1, 99, 87, 69, 56, 41, 33, 21, 15, 8, 4, 1, 127, 99, 87, 69, 56, 41, 33, 21, 15, 8, 4, 1

Offset: 1

Omar E. Pol, Jan 09 2022

T(n,k) is the number of cubic cells (or cubes) in the k-th level starting from the base of the stepped pyramid with n levels described in A245092 (see example).

			Triangle begins:
    1;
    4,  1;
    8,  4,  1;
   15,  8,  4,  1;
   21, 15,  8,  4,  1;
   33, 21, 15,  8,  4,  1;
   41, 33, 21, 15,  8,  4,  1;
   56, 41, 33, 21, 15,  8,  4,  1;
   69, 56, 41, 33, 21, 15,  8,  4,  1;
   87, 69, 56, 41, 33, 21, 15,  8,  4,  1;
   99, 87, 69, 56, 41, 33, 21, 15,  8,  4,  1;
  127, 99, 87, 69, 56, 41, 33, 21, 15,  8,  4,  1;
...
For n = 9 the lateral view and top view of the stepped pyramid described in A245092 look as shown below:
                        _
     9        1        |_|_
     8        4        |_ _|_
     7        8        |_ _|_|_
     6       15        |_ _ _| |_
     5       21        |_ _ _|_ _|_
     4       33        |_ _ _ _| | |_
     3       41        |_ _ _ _|_|_ _|_
     2       56        |_ _ _ _ _|_|_  |_
     1       69        |_ _ _ _ _|_ _|_ _|
.
   Level   Row 9         Lateral view of
     k     T(9,k)      the stepped pyramid
.
                        _ _ _ _ _ _ _ _ _
                       |_| | | | | | | | |
                       |_ _|_| | | | | | |
                       |_ _|  _|_| | | | |
                       |_ _ _|    _|_| | |
                       |_ _ _|  _|  _ _|_|
                       |_ _ _ _|  _| |
                       |_ _ _ _| |_ _|
                       |_ _ _ _ _|
                       |_ _ _ _ _|
.
                           Top view of
                       the stepped pyramid
.
For n = 9 and k = 1 there are 69 cubic cells in the level 1 starting from the base of the stepped pyramid, so T(9,1) = 69.
For n = 9 and k = 9 there is only one cubic cell in the level k = 9 (the top) of the stepped pyramid, so T(9,9) = 1.
The volume of the stepped pyramid (also the total number of cubic cells) represents the 9th term of the convolution of A000203 and A000027 hence it's equal to A175254(9) = 248, equaling the sum of the 9th row of triangle.

Omar E. Pol, Perspective view of the stepped pyramid (first 16 levels)

Column k gives A024916 starting in row k.
Row sums give A175254.
Cf. A340423 (analog for the tower described in A221529).
Cf. A000027, A000203, A004736, A196020, A235791, A236104, A237591, A237593, A245092, A262626, A272172.

Join@@Array[Reverse@Array[Sum[#-Mod[#,m],{m,#}]&,#]&,12] (* Giorgos Kalogeropoulos, Jan 12 2022 *)

row(n) = Vecrev(vector(n, k, sum(i=1, k, k\i*i))); \\ Michel Marcus, Jan 22 2022

T(n,k) = A024916(A004736(n,k)).
T(n,k) = T(n,k) = A024916(n-k+1).
T(n,k) = Sum_{j=1..n} A272172(j,k).

A379635 Triangle read by rows: T(n,k) = A000203(k)*A000203(n-k+1), n >= 1, k >= 1.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 7, 12, 12, 7, 6, 21, 16, 21, 6, 12, 18, 28, 28, 18, 12, 8, 36, 24, 49, 24, 36, 8, 15, 24, 48, 42, 42, 48, 24, 15, 13, 45, 32, 84, 36, 84, 32, 45, 13, 18, 39, 60, 56, 72, 72, 56, 60, 39, 18, 12, 54, 52, 105, 48, 144, 48, 105, 52, 54, 12, 28, 36, 72, 91, 90, 96, 96, 90, 91, 72, 36, 28

Offset: 1

Omar E. Pol, Jan 14 2025

			Triangle begins:
   1;
   3,   3;
   4,   9,   4;
   7,  12,  12,   7;
   6,  21,  16,  21,   6;
  12,  18,  28,  28,  18,  12;
   8,  36,  24,  49,  24,  36,   8;
  15,  24,  48,  42,  42,  48,  24,  15;
  13,  45,  32,  84,  36,  84,  32,  45,  13;
  18,  39,  60,  56,  72,  72,  56,  60,  39,  18;
  12,  54,  52, 105,  48, 144,  48, 105,  52,  54,  12;
  28,  36,  72,  91,  90,  96,  96,  90,  91,  72,  36,  28;
  14,  84,  48, 126,  78, 180,  64, 180,  78, 126,  48,  84,  14;
  ...
For n = 10 the calculation of the row 10 is as follows:
    k    A000203         T(10,k)
    1       1   *  18   =   18
    2       3   *  13   =   39
    3       4   *  15   =   60
    4       7   *   8   =   56
    5       6   *  12   =   72
    6      12   *   6   =   72
    7       8   *   7   =   56
    8      15   *   4   =   60
    9      13   *   3   =   39
   10      18   *   1   =   18
                 A000203
.

Index entries for sequences related to sigma(n).

Column 1 and leading diagonal give A000203.
Middle diagonal gives A072861.
Row sums give A000385.
Cf. A221529.

T[n_,k_]:=DivisorSigma[1,k]*DivisorSigma[1,n-k+1];Table[T[n,k],{n,12},{k,n }]//Flatten (* James C. McMahon, Jan 15 2025 *)

PARI
```
T(n, k)=sigma(k)*sigma(n-k+1)
```

A380231 Alternating row sums of triangle A237591.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Jan 17 2025

Consider the symmetric Dyck path in the first quadrant of the square grid described in the n-th row of A237593. Let C = (A240542(n), A240542(n)) be the middle point of the Dyck path.
a(n) is also the coordinate on the x axis of the point (a(n),n) and also the coordinate on the y axis of the point (n,a(n)) such that the middle point of the line segment [(a(n),n),(n,a(n))] coincides with the middle point C of the symmetric Dyck path.
The three line segments [(a(n),n),C], [(n,a(n)),C] and [(n,n),C] have the same length.
For n > 2 the points (n,n), C and (a(n),n) are the vertices of a virtual isosceles right triangle.
For n > 2 the points (n,n), C and (n,a(n)) are the vertices of a virtual isosceles right triangle.
For n > 2 the points (a(n),n), (n,n) and (n,a(n)) are the vertices of a virtual isosceles right triangle.

			For n = 14 the 14th row of A237591 is [8, 3, 1, 2] hence the alternating row sum is 8 - 3 + 1 - 2 = 4, so a(14) = 4.
On the other hand the 14th row of A237593 is the 14th row of A237591 together with the 14 th row of A237591 in reverse order as follows: [8, 3, 1, 2, 2, 1, 3, 8].
Then with the terms of the 14th row of A237593 we can draw a Dyck path in the first quadrant of the square grid as shown below:
.
         (y axis)
          .
          .
          .    (4,14)              (14,14)
          ._ _ _ . _ _ _ _            .
          .               |
          .               |
          .               |_
          .                 |
          .                 |_ _
          .                C    |_ _ _
          .                           |
          .                           |
          .                           |
          .                           |
          .                           . (14,4)
          .                           |
          .                           |
          . . . . . . . . . . . . . . | . . . (x axis)
        (0,0)
.
In the example the point C is the point (9,9).
The three line segments [(4,14),(9,9)], [(14,4),(9,9)] and [(14,14),(9,9)] have the same length.
The points (14,14), (9,9) and (4,14) are the vertices of a virtual isosceles right triangle.
The points (14,14), (9,9) and (14,4) are the vertices of a virtual isosceles right triangle.
The points (4,14), (14,14) and (14,4) are the vertices of a virtual isosceles right triangle.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Other alternating row sums (ARS) related to the Dyck paths of A237593 and the stepped pyramid described in A245092 are as follows:
ARS of A237593 give A000004.
ARS of A196020 give A000203.
ARS of A252117 give A000203.
ARS of A271343 give A000593.
ARS of A231347 give A001065.
ARS of A236112 give A004125.
ARS of A236104 give A024916.
ARS of A249120 give A024916.
ARS of A271344 give A033879.
ARS of A231345 give A033880.
ARS of A239313 give A048050.
ARS of A237048 give A067742.
ARS of A236106 give A074400.
ARS of A235794 give A120444.
ARS of A266537 give A146076.
ARS of A236540 give A153485.
ARS of A262612 give A175254.
ARS of A353690 give A175254.
ARS of A239446 give A235796.
ARS of A239662 give A239050.
ARS of A235791 give A240542.
ARS of A272026 give A272027.
ARS of A211343 give A336305.
Cf. A221529, A237270, A237271, A237591, A262626, A322141.

A380231[n_] := 2*Sum[(-1)^(k + 1)*Ceiling[(n + 1)/k - (k + 1)/2], {k,  Quotient[Sqrt[8*n + 1] - 1, 2]}] - n;
Array[A380231 , 100] (* Paolo Xausa, Sep 06 2025 *)

row235791(n) = vector((sqrtint(8*n+1)-1)\2, i, 1+(n-(i*(i+1)/2))\i);
a(n) = my(orow = concat(row235791(n), 0)); vecsum(vector(#orow-1, i, (-1)^(i+1)*(orow[i] - orow[i+1]))); \\ Michel Marcus, Apr 13 2025

a(n) = 2*A240542(n) - n.
a(n) = n - 2*A322141(n).
a(n) = A240542(n) - A322141(n).

cp's OEIS Frontend

A346562 Irregular triangle read by rows in which row n lists the first n - 2 terms of A000005 together with the sum of A000005(n-1) and A000005(n), with a(1) = 1.

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A350333 Irregular triangle read by rows in which row n lists all elements of the arrangement of the correspondence divisor/part related to the partitions of n in the following order: row n lists the n-th row of A026792 followed by the n-th row of A338156.

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A350357 Irregular triangle read by rows in which row n lists all elements of the arrangement of the correspondence divisor/part related to the last section of the set of partitions of n in the following order: row n lists the n-th row of A138121 followed by the n-th row of A336812.

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A384230 Number of subparts in the central part of the symmetric representation of sigma(n).

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A350637 Triangle read by rows: T(n,k) in which row n lists the first n terms of A024916 in reverse order, 1 <= k <= n.

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A379635 Triangle read by rows: T(n,k) = A000203(k)*A000203(n-k+1), n >= 1, k >= 1.

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A380231 Alternating row sums of triangle A237591.

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