cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A240061 Triangle read by rows, n>=1, 1<=k<=n. T(n,k) = number of cells in k-th row = number of cells in the k-th column of the diagram of the symmetric representation of sigma(n) in the first quadrant.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 0, 3, 1, 1, 1, 3, 2, 4, 1, 1, 1, 1, 0, 0, 4, 1, 1, 1, 1, 3, 2, 1, 5, 1, 1, 1, 1, 1, 1, 2, 0, 5, 1, 1, 1, 1, 1, 3, 1, 2, 1, 6, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 6, 1, 1, 1, 1, 1, 1, 4, 3, 4, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 7
Offset: 1

Views

Author

Omar E. Pol, Apr 26 2014

Keywords

Comments

Since the diagram is symmetric the number of cells in the k-th row equals the number of cells in k-th column, see example.
Row sums give A000203.
Right border gives A008619, n >= 1.
If n is an odd prime then row n lists (n+1)/2 ones, ((n+1)/2 - 2) zeros, and (n+1)/2.

Examples

			Triangle begins:
1;
1, 2;
1, 1, 2;
1, 1, 2, 3;
1, 1, 1, 0, 3;
1, 1, 1, 3, 2, 4;
1, 1, 1, 1, 0, 0, 4;
1, 1, 1, 1, 3, 2, 1, 5;
1, 1, 1, 1, 1, 1, 2, 0, 5;
1, 1, 1, 1, 1, 3, 1, 2, 1, 6;
1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 6;
1, 1, 1, 1, 1, 1, 4, 3, 4, 3, 1, 7;
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 7;
...
For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this:
y
.                               Number of cells
._ _ _ _ _
|_ _ _ _ _|                            5
.         |_ _                         0
.         |_  |                        2
.           |_|_ _                     1
.               | |                    1
.               | |                    1
.               | |                    1
.               | |                    1
. . . . . . . . |_| . . x              1
.
So the 9th row of triangle is [1, 1, 1, 1, 1, 1, 2, 0, 5].
For n = 9 and k = 7 there are two cells in the 7th row of the diagram, also there are two cells in the 7th column of the diagram, so T(9,7) = 2.

Links

Crossrefs

Cf. A000203, A008619, A024916, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A240060.

A252922 a(n) = sigma(n-1) + sigma(n-2) + sigma(n-3), with a(1)=0, a(2)=1, a(3)=4.

Original entry on oeis.org

0, 1, 4, 8, 14, 17, 25, 26, 35, 36, 46, 43, 58, 54, 66, 62, 79, 73, 88, 77, 101, 94, 110, 92, 120, 115, 133, 113, 138, 126, 158, 134, 167, 143, 165, 150, 193, 177, 189, 154, 206, 188, 228, 182, 224, 206, 234, 198, 244, 229, 274, 222, 263, 224, 272, 246, 312, 272, 290, 230, 318, 290, 326, 262, 327, 315, 355, 296
Offset: 1

Views

Author

Omar E. Pol, Dec 24 2014

Keywords

Comments

This is also a rectangular array read by rows, with four columns, in which T(j,k) is the number of cells (also the area) of the j-th gap between the arms in the k-th quadrant of the spiral of the symmetric representation of sigma described in A239660, with j >= 1 and 1 <= k <= 4 and starting with T(1,1) = 0, see example.
We can find the spiral (mentioned above) on the terraces of the stepped pyramid described in A244050. - Omar E. Pol, Dec 07 2016

Examples

			a(5) = sigma(4) + sigma(3) + sigma(2) = 7 + 4 + 3 = 14. On the other hand a(5) = A024916(4) - A024916(1) = 15 - 1 = 14.
...
Also, if written as a rectangular array T(j,k) with four columns the sequence begins:
    0,   1,   4,   8;
   14,  17,  25,  26;
   35,  36,  46,  43;
   58,  54,  66,  62;
   79,  73,  88,  77;
  101,  94, 110,  92;
  120, 115, 133, 113;
  138, 126, 158, 134;
  167, 143, 165, 150;
  193, 177, 189, 154;
  206, 188, 228, 182;
  224, 206, 234, 198;
  244, 229, 274, 222;
  263, 224, 272, 246;
  312, 272, 290, 230;
  318, 290, 326, 262;
  ...
In this case T(2,1) = a(5) = 14.

Links

Crossrefs

Cf. A000203, A010883, A024916, A092403, A112610, A193553, A196020, A236104, A237270, A237271, A237593, A239052, A239053, A239931-A239934, A239660, A240020, A244050, A245092, A262626.

Programs

  • Maple
    L:= [0,0,0,seq(numtheory:-sigma(n), n=1..100)]:
L[1..101]+L[2..102]+L[3..103]; # Robert Israel, Dec 07 2016
  • Mathematica
    a252922[n_] := Block[{f}, f[1] = 0; f[2] = 1; f[3] = 4;
  f[x_] := DivisorSigma[1, x - 1] + DivisorSigma[1, x - 2] +
DivisorSigma[1, x - 3]; Table[f[i], {i, n}]]; a252922[68] (* Michael De Vlieger, Dec 27 2014 *)
  • PARI
    v=concat([0,1,4],vector(100,n,sigma(n)+sigma(n+1)+sigma(n+2))) \\ Derek Orr, Dec 30 2014

Formula

a(1) = 0, a(2) = sigma(1) = 1, a(3) = sigma(2) + sigma(1) = 4; for n >= 4, a(n) = sigma(n-1) + sigma(n-2) + sigma(n-3).
a(n) = A024916(n-1) - A024916(n-4) for n >= 5.

A265999 Numbers k such that in the symmetric representation of sigma(k) all parts are of the same size.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 52, 53, 54, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 71, 72, 73, 74, 76, 78, 79, 80, 82, 83, 84, 86, 88, 89, 90, 92, 94, 96, 97, 100
Offset: 1

Views

Author

Omar E. Pol, Dec 19 2015

Keywords

Comments

All powers of 2, all prime numbers and all even perfect numbers are members of this sequence.
For more information about the symmetric representation of sigma see A237270 and A237593.
Sequence A174973: the symmetric representation of sigma, SRS(A174973(n)) consisting of 1 part, and sequence A239929: SRS(A239929(n)) consisting of 2 parts, are proper subsequences. Sequence A251820: SRS(A251820(n)) consisting of 3 equal parts, contains the only other known members 15 and 5950 of this sequence. No number m with SRS(m) consisting of 4 or more equal parts is known. - Hartmut F. W. Hoft, Jan 11 2025

Examples

			9 is not in the sequence because the parts of the symmetric representation of sigma(9) = 13 are [5, 3, 5].
10 is in the sequence because the parts of the symmetric representation of sigma(10) = 18 are [9, 9].
SRS(15) = { 8, 8, 8 } and SRS(5950) = { 4464, 4464, 4464 }. - _Hartmut F. W. Hoft_, Jan 11 2025

Links

Crossrefs

Cf. A000040, A000079, A000203, A000396, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A245092, A262626, A266000.
Cf. A174973, A239929, A251820, A377654.

Programs

  • Mathematica
    (* Function partsSRS[ ] is defined in A377654 *)
a265999[n_] := Select[Range[n], Length[Union[partsSRS[#]]]==1&]
a265999[100] (* Hartmut F. W. Hoft, Jan 11 2025 *)

A266000 Numbers k such that the symmetric representation of sigma(k) has at least two parts of distinct size.

Original entry on oeis.org

9, 21, 25, 27, 33, 35, 39, 45, 49, 50, 51, 55, 57, 63, 65, 69, 70, 75, 77, 81, 85, 87, 91, 93, 95, 98, 99, 105, 110, 111, 115, 117, 119, 121, 123, 125, 129, 130, 133, 135, 141, 143, 145, 147, 153, 154, 155, 159, 161, 165, 169, 170, 171, 175, 177, 182, 183, 185, 187, 189, 190, 195
Offset: 1

Views

Author

Omar E. Pol, Dec 19 2015

Keywords

Comments

In other words: numbers k such that the symmetric representation of sigma(k) has at least two parts with distinct number of cells.
For more information about the symmetric representation of sigma see A237270 and A237593.
When the symmetric representation of sigma of m, SRS(m), consists of 2n-1 or 2n parts, n>=1, then at most n parts can be of distinct sizes. For the published terms in A239663, SRS(A239663(n)) consists of n parts representing ceiling(n/2) parts of distinct sizes, n>=1. Only two numbers m are known, 15 and 5950 in A251820, for which SRS(m) consists of n parts of less than ceiling(n/2) distinct sizes. - Hartmut F. W. Hoft, Jan 11 2025

Examples

			The symmetric representation of sigma(9) = 13 in the first quadrant looks like this:
y
.
._ _ _ _ _ 5
|_ _ _ _ _|
.         |_ _ 3
.         |_  |
.           |_|_ _ 5
.               | |
.               | |
.               | |
.               | |
. . . . . . . . |_| . . x
.
There are three parts: 5 + 3 + 5 = 13, so 9 is in the sequence because the structure contains at least two parts of distinct size.
From _Hartmut F. W. Hoft_, Jan 11 2025: (Start)
SRS(a(1)) = SRS(A239663(3)) = SRS(9) = { 5, 3, 5 } is the smallest with 2 parts of distinct sizes.
SRS(a(14)) = SRS(A239663(5)) = SRS(63) = { 32, 12, 16, 12, 32 } is the smallest with 3 parts of distinct sizes.
SRS(a(127)) = SRS(A239663(7)) = SRS(357) = { 179, 61, 29, 38, 29, 61, 179 } is the smallest with 4 parts of distinct sizes. (End)

Crossrefs

Complement of A265999.
Cf. A000203, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A245092, A262626.
Cf. A239663, A251820, A377654.

Programs

  • Mathematica
    (* Function partsSRS[ ] is defined in A377654 *)
a266000[n_] := Select[Range[n], Length[Union[partsSRS[#]]]>=2&]
a266000[200] (* Hartmut F. W. Hoft, Jan 11 2025 *)

Extensions

Extended from a(37) to a(62) by Hartmut F. W. Hoft, Jan 11 2025

A343621 Numbers k such that the largest Dyck path of the symmetric representation of sigma(k) does not touch the largest Dyck path of the symmetric representation of sigma(k+1).

Original entry on oeis.org

1, 3, 5, 7, 11, 15, 17, 19, 23, 27, 29, 31, 35, 39, 41, 47, 53, 55, 59, 63, 65, 71, 79, 83, 87, 89, 95, 99, 103, 107, 111, 119, 125, 127, 131, 139, 143, 149, 155, 159, 161, 167, 175, 179, 191, 195, 197, 199, 203, 207, 209, 215, 219, 223, 227, 233, 239, 251, 255
Offset: 1

Views

Author

Omar E. Pol, Aug 04 2021

Keywords

Comments

This property of a(n) is because the symmetric representation of sigma(a(n)+1) has only one part.
All terms are odd.
First differs from A085493 at a(22).

Links

Crossrefs

Cf. A000203, A085493, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239931, A239932, A239933, A239934, A262626, A343621.

Programs

  • Mathematica
    (* Functions a174973Q[ ] is defined in A279029 *)
a343621[n_] := Select[Range[n], a174973Q[#+1]&]
a343621[255] (* Hartmut F. W. Hoft, Feb 20 2025 *)

Formula

a(n) = A174973(n+1) - 1.

A348854 a(n) is the total length of all line segments in an octant of the symmetric representation of sigma(n).

Original entry on oeis.org

2, 4, 6, 8, 9, 12, 12, 16, 17, 20, 18, 24, 21, 27, 28, 32, 27, 36, 30, 40, 39, 41, 36, 48, 42, 48, 49, 56, 45, 60, 48, 64
Offset: 1

Views

Author

Omar E. Pol, Nov 01 2021

Keywords

Comments

One half of the total length of all line segments of the symmetric representation of sigma(n).
If the symmetric representation of sigma(n) has only one part (cf. A174973) or if it has two parts and they meet at the center of the Dyck path (cf. A262259) then a(n) = 2*n, otherwise a(n) < 2*n. In other words: if n is a term of A279029 then a(n) = 2*n, otherwise a(n) < 2*n.

Crossrefs

Cf. A005843 (upper bounds).
For illustrations see A348705.
Cf. A174973, A235791, A236104, A237270, A237271, A237591, A237593, A238443, A239660, A239931-A239934, A245092, A262259, A279029.

Formula

a(n) = A348705(n)/2.

A240060 Triangle read by rows, n>=1, 1<=k<=n. T(n,n-k+1) = number of cells in the k-th row = number of cells in the k-th column of the diagram of the symmetric representation of sigma(n) in the first quadrant.

Original entry on oeis.org

1, 2, 1, 2, 1, 1, 3, 2, 1, 1, 3, 0, 1, 1, 1, 4, 2, 3, 1, 1, 1, 4, 0, 0, 1, 1, 1, 1, 5, 1, 2, 3, 1, 1, 1, 1, 5, 0, 2, 1, 1, 1, 1, 1, 1, 6, 1, 2, 1, 3, 1, 1, 1, 1, 1, 6, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 7, 1, 3, 4, 3, 4, 1, 1, 1, 1, 1, 1, 7, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Omar E. Pol, Apr 26 2014

Keywords

Comments

Since the diagram is symmetric the number of cells in the k-th row equals the number of cell in the k-th column, see example.
Row sums give A000203.
Column 1 gives A008619, n >= 1.
If n is an odd prime then row n lists (n+1)/2, ((n+1)/2 - 2) zeros, and (n+1)/2 ones.
Mirror of A240061.

Examples

			Triangle begins:
1;
2, 1;
2, 1, 1;
3, 2, 1, 1;
3, 0, 1, 1, 1;
4, 2, 3, 1, 1, 1;
4, 0, 0, 1, 1, 1, 1;
5, 1, 2, 3, 1, 1, 1, 1;
5, 0, 2, 1, 1, 1, 1, 1, 1;
6, 1, 2, 1, 3, 1, 1, 1, 1, 1;
6, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1;
7, 1, 3, 4, 3, 4, 1, 1, 1, 1, 1, 1;
7, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1;
...
For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this:
y
.                               Number of cells
._ _ _ _ _
|_ _ _ _ _|                            5
.         |_ _                         0
.         |_  |                        2
.           |_|_ _                     1
.               | |                    1
.               | |                    1
.               | |                    1
.               | |                    1
. . . . . . . . |_| . . x              1
.
So the 9th row of triangle is [5, 0, 2, 1, 1, 1, 1, 1, 1].
For n = 9 and k = 7 there are two cells in the 7th row of the diagram, also there are two cells in the 7th column of the diagram, so T(9,9-7+1) = T(9,3) = 2.

Links

Crossrefs

Cf. A000203, A008619, A024916, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A240061.

A317308 Primes p such that the largest Dyck path of the symmetric representation of sigma(p) has a central peak.

Original entry on oeis.org

2, 7, 17, 19, 29, 31, 47, 53, 67, 71, 73, 97, 101, 103, 127, 131, 157, 163, 167, 191, 193, 197, 199, 233, 239, 241, 251, 277, 281, 283, 293, 331, 337, 347, 349, 379, 383, 389, 397, 401, 439, 443, 449, 457, 461, 463, 499, 503, 509, 521, 523, 563, 569, 571, 577, 587, 593, 631, 641, 643, 647, 653, 659, 661
Offset: 1

Views

Author

Omar E. Pol, Aug 29 2018

Keywords

Comments

Also primes p such that both Dyck paths of the symmetric representation of sigma(p) have a central peak.
Note that the symmetric representation of sigma of an odd prime consists of two perpendicular bars connected by an irregular zig-zag path (see example).
Odd primes and the terms of this sequence are easily identifiable in the pyramid described in A245092 (see Links section).
For more information about the mentioned Dyck paths see A237593.
Equivalently, primes p such that the largest Dyck path of the symmetric representation of sigma(p) has an odd number of peaks.

Examples

			Illustration of initial terms:
--------------------------------------------------------
   p   sigma(p)   Diagram of the symmetry of sigma
--------------------------------------------------------
                    _         _                   _   _
                  _| |       | |                 | | | |
   2      3      |_ _|       | |                 | | | |
                             | |                 | | | |
                            _|_|                 | | | |
                          _|                     | | | |
                  _ _ _ _|                       | | | |
   7      8      |_ _ _ _|                       | | | |
                                                 | | | |
                                            _ _ _|_| | |
                                           |    _ _ _|_|
                                          _|   |
                                        _|  _ _|
                                    _ _|  _|
                                   |     |
                                   |  _ _|
                  _ _ _ _ _ _ _ _ _| |
  17     18      |_ _ _ _ _ _ _ _ _| |
                  _ _ _ _ _ _ _ _ _ _|
  19     20      |_ _ _ _ _ _ _ _ _ _|
.
For the first four terms of the sequence we can see in the above diagram that the largest Dyck path of the symmetric representation of sigma(p) has a central peak.
Compare with A317309.

Links

Crossrefs

Primes in A162917.
Also primes in A317303.
The union of this sequence and A317309 gives A000040.
Cf. A000203, A065091, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A239660, A239929, A239931, A239933, A244050, A245092, A262626.

A317309 Primes p such that the largest Dyck path of the symmetric representation of sigma(p) has a central valley.

Original entry on oeis.org

3, 5, 11, 13, 23, 37, 41, 43, 59, 61, 79, 83, 89, 107, 109, 113, 137, 139, 149, 151, 173, 179, 181, 211, 223, 227, 229, 257, 263, 269, 271, 307, 311, 313, 317, 353, 359, 367, 373, 409, 419, 421, 431, 433, 467, 479, 487, 491, 541, 547, 557, 599, 601, 607, 613, 617, 619, 673, 677, 683, 691, 701
Offset: 1

Views

Author

Omar E. Pol, Aug 29 2018

Keywords

Comments

Except for the first term 3, primes p such that both Dyck paths of the symmetric representation of sigma(p) have a central valley.
Note that the symmetric representation of sigma of an odd prime consists of two perpendicular bars connected by an irregular zig-zag path (see example).
Odd primes and the terms of this sequence are easily identifiable in the pyramid described in A245092 (see Links section).
For more information about the mentioned Dyck paths see A237593.
Equivalently, primes p such that the largest Dyck path of the symmetric representation of sigma(p) has an even number of peaks.

Examples

			Illustration of initial terms:
-------------------------------------------------
   p  sigma(p)  Diagram of the symmetry of sigma
-------------------------------------------------
                     _   _           _   _
                    | | | |         | | | |
                 _ _|_| | |         | | | |
   3      4     |_ _|  _|_|         | | | |
                 _ _ _|             | | | |
   5      6     |_ _ _|             | | | |
                                 _ _|_| | |
                               _|    _ _|_|
                             _|     |
                            |      _|
                 _ _ _ _ _ _|  _ _|
  11     12     |_ _ _ _ _ _| |
                 _ _ _ _ _ _ _|
  13     14     |_ _ _ _ _ _ _|
.
For the first four terms of the sequence we can see in the above diagram that the largest Dyck path of the symmetric representation of sigma(p) has a central valley.
Compare with A317308.

Links

Crossrefs

Primes in A161983.
Except for the first term 3, primes in A317304.
The union of A317308 and this sequence gives A000040.
Primes of the triangle of A060300. - César Aguilera, Nov 12 2020
Cf. A000203, A065091, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A239660, A239929, A239931, A239933, A244050, A245092, A262626.

Programs

  • Python
    from sympy import isprime
for x in range(1,100):
     for x in range(2*x**2+2*x-(2*x//2),2*x**2+2*x+(2*x//2)+1):
           if isprime(x):
              print(x, end=', ') # César Aguilera, Nov 12 2020

A356351 Partial sums of the ziggurat sequence A347186.

Original entry on oeis.org

1, 5, 11, 27, 39, 76, 96, 160, 196, 286, 328, 489, 545, 701, 808, 1064, 1154, 1488, 1598, 2006, 2208, 2550, 2706, 3403, 3610, 4072, 4384, 5169, 5409, 6385, 6657, 7681, 8127, 8883, 9324, 10910, 11290, 12220, 12824, 14560, 15022, 16863, 17369, 19175, 20276, 21608, 22208, 25129, 25849, 27669
Offset: 1

Views

Author

Omar E. Pol, Oct 15 2022

Keywords

Comments

a(n) is the volume (or the number of cubes) in a polycube whose base is the symmetric representation of A024916(n) which is formed with the first n 3D-Ziggurats described in A347186.
a(n) is also the total number of cubes in a three-dimensional spiral formed with the first n 3D-Ziggurats described in A347186 (see example). The base of the 3D-spiral is the spiral formed with the symmetric representation of sigma of the first n positive integers as shown in the example section of A239660.

Examples

			For n = 16 the figure shows the top view of a three-dimensional spiral formed with the first 16 3D-Ziggurats described in A347186. There are four 3D-Ziggurats in every quadrant:
.
                  _ _ _ _ _ _ _ _
                 |_|_|_|_|_|_|_|_|_ _ _ _ _ _ _
                 |_|             |_|_|_|_|_|_|_|
                _|_|                           |
               |_|_|  _ _ _ _ _ _              |_ _
            _ _|     |_|_|_|_|_|_|_ _ _ _ _        |_
      _ _ _|_|      _|_|         |_|_|_|_|_|         |
     |_|_|_|_|    _|_|_|                   |_ _      |_ _ _
     |_|      _ _|_|      _ _ _ _          |_|_|         |_|
     |_|     |_|_|_|    _|_|_|_|_|_ _ _      |_|_ _      |_|
     |_|     |_|      _|_|_|     |_|_|_|         |_|     |_|
     |_|     |_|     |_|_|_|           |_ _      |_|     |_|
     |_|     |_|     |_|      _ _        |_|     |_|     |_|
     |_|     |_|     |_|     |_|_|_      |_|     |_|     |_|
    _|_|    _|_|    _|_|    _|_| |_|    _|_|    _|_|    _|_|    _
   |_|     |_|     |_|     |_|         |_|     |_|     |_|     |_|
   |_|     |_|     |_|     |_|_ _     _|_|     |_|     |_|     |_|
   |_|     |_|     |_|       |_|_|_ _|_|_|     |_|     |_|     |_|
   |_|     |_|     |_|_          |_|_|_|    _ _|_|     |_|     |_|
   |_|     |_|         |_                 _|_|_|_|     |_|     |_|
   |_|     |_|_ _        |_ _ _ _        |_|_|    _ _ _|_|     |_|
   |_|           |_      |_|_|_|_|_ _ _ _|_|    _|_|_|_|_|     |_|
   |_|_ _ _        |_            |_|_|_|_|_|  _|_|_|_|    _ _ _|_|
         |_|_ _      |                       |_|_|_|_|   |_|_|_|_|
         |_|_|_|     |_ _ _ _ _ _            |_|_|_|    _|_|
           |_|_|_    |_|_|_|_|_|_|_ _ _ _ _ _|_|      _|_|_|
             |_|_|               |_|_|_|_|_|_|_|  _ _|_|_|
                 |                               |_|_|_|
                 |_ _ _ _ _ _ _ _                |_|
                 |_|_|_|_|_|_|_|_|_ _ _ _ _ _ _ _|_|
                                 |_|_|_|_|_|_|_|_|_|
.
The number of square cells in the top view of the n-th 3D-Ziggurat equals A000203(n).
The total number of square cells in the top view of the 3D-Spiral with the first n 3D-Ziggurats equals A024916(n).
In the above figure the total number of square cells equals A024916(16) = 220.
a(16) = 1064 is the total number of cubes in the 3D-Spiral with the first 16 3D-Ziggurats.

Crossrefs

Cf. A000203, A024916, A196020, A235791, A236104, A237270, A237591, A237593, A239660, A239931, A239932, A239933, A239934, A347186, A296508, A299778, A347186, A347263, A347367, A347529, A351819.
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