A333029 -id:A333029 - cp's OEIS frontend

A361993 (2,1)-block array, B(2,1), of the Wythoff array (A035513), read by descending antidiagonals.

5, 9, 15, 14, 25, 26, 23, 40, 43, 36, 37, 65, 69, 59, 47, 60, 105, 112, 95, 77, 57, 97, 170, 181, 154, 124, 93, 68, 157, 275, 293, 249, 201, 150, 111, 78, 254, 445, 474, 403, 325, 243, 179, 127, 89, 411, 720, 767, 652, 526, 393, 290, 205, 145, 99, 665, 1165

Offset: 1

Clark Kimberling, Apr 04 2023

We begin with a definition. Suppose that W = (w(i,j)), where i >= 1 and j >= 1, is an array of numbers such that if m and n satisfy 1 <= m < n, then there exists k such that w(m,k+h) < w(n,h+1) < w(m,k+h+1) for every h >= 0. Then W is a row-splitting array. The array B(2,1) is a row-splitting array. The rows of B(2,1) are linearly recurrent with signature (1,1); the columns are linearly recurrent with signature (1,1,-1). The order array (as defined in A333029) of B(2,1) is A361995.

			Corner of B(2,1):
   5    9   14   23   37   60   97  157 ...
  15   25   40   65  105  170  275  445 ...
  26   43   69  112  181  293  474  767 ...
  36   59   95  154  249  403  652 1055 ...
  47   77  124  202  325  526  851 1377 ...
  ...
(column 1 of A035513) = (1,4,6,9,12,14,17,19,...), so (column 1 of B(2,1)) = (5,15,26,36,...);
(column 2 of A000027) = (2,7,10,15,20,23,28,31,...), so (column 2 of B(2,1)) = (9,25,43,59,...).

Cf. A000045, A001622, A035513, A080164, A361975, A361992 (array B(1,2)), A361994 (array B(2,2)).

f[n_] := Fibonacci[n]; r = GoldenRatio;
zz = 10; z = 13;
w[n_, k_] := f[k + 1] Floor[n*r] + (n - 1) f[k]
t[h_, k_] := w[2 h - 1, k] + w[2 h, k];
Table[t[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A361993 sequence *)
TableForm[Table[t[h, k], {h, 1, zz}, {k, 1, z}]] (* A361993 array *)

B(2,1) = (b(i,j)), where b(i,j) = w(2i-1,j) + w(2i,j) for i >= 1, j >= 1, where (w(i,j)) is the Wythoff array (A035513).

b(i,j) = F(j+1) ([2 i r] + [(2 i - 1) r]) + (4 i - 3) F(j), where F = A000045, the Fibonacci numbers, and r = (1+sqrt(5))/2, the golden ratio, A001622, and [ ] = floor.

A333028 Array consisting of the primitive rows of the Wythoff array (A035513), read by antidiagonals.

Original entry on oeis.org

1, 2, 4, 3, 7, 14, 5, 11, 23, 17, 8, 18, 37, 28, 19, 13, 29, 60, 45, 31, 25, 21, 47, 97, 73, 50, 41, 27, 34, 76, 157, 118, 81, 66, 44, 30, 55, 123, 254, 191, 131, 107, 71, 49, 35, 89, 199, 411, 309, 212, 173, 115, 79, 57, 43, 144, 322, 665, 500, 343, 280

Offset: 1

Clark Kimberling, Mar 10 2020

In a row of the Wythoff array, either every two consecutive terms are relatively prime or else no two consecutive terms are relatively prime. In the first case, we call the row primitive; otherwise, the row is an integer multiple of a tail of a preceding row. The primitive rows are interspersed, in the sense that if h < k then the numbers in row k are interspersed, in magnitude, among numbers in row h. In each row, every pair of consecutive numbers is a Wythoff pair of relatively prime numbers. The array includes every prime.

			Northwest corner:
   1   2   3    5    8   13  21    34
   4   7  11   18   29   47  76   123
  14  23  37   60   97  157  254  411
  17  28  45   73  118  191  309  500
  19  31  50   81  131  212  343  555
  25  41  66  107  173  280  453  733
  27  44  71  115  186  301  487  788
  30  49  79  128  207  335  542  877

Cf. A000045, A000032, A332937, A332938, A333029, A333086.

W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 160}]
u = Flatten[Position[t, 1]]; v[n_, k_] := W[u[[n]], k];
TableForm[Table[v[n, k], {n, 1, 30}, {k, 1, 8}]] (* A333028 array *)
Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* A333028 sequence *)

A361974 (1,2)-block array, B(1,2), of the natural number array (A000027), read by descending antidiagonals.

Original entry on oeis.org

3, 11, 8, 27, 20, 15, 51, 40, 31, 24, 83, 68, 55, 44, 35, 123, 104, 87, 72, 59, 48, 171, 148, 127, 108, 91, 76, 63, 227, 200, 175, 152, 131, 112, 95, 80, 291, 260, 231, 204, 179, 156, 135, 116, 99, 363, 328, 295, 264, 235, 208, 183, 160, 139, 120, 443, 404

Offset: 1

Clark Kimberling, Apr 01 2023

We begin with a definition. Suppose that W = (w(i,j)), where i >= 1 and j >= 1, is an array of numbers such that if m and n satisfy 1 <= m < n, then there exists k such that w(m,k+h) < w(n,h+1) < w(m,k+h+1) for every h >= 0. Then W is a row-splitting array. The array B(1,2) is a row-splitting array. The rows and columns of B(1,2) are linearly recurrent with signature (3,-3,1). It appears that the order array (as defined in A333029) of B(1,2) is given by A163255.

			Corner of B(1,2):
   3   11   27   51   83  123   171   227
   8   20   40   68  104  148   200   260
  15   31   55   87  127  175   231   295
  24   44   72  108  152  204   264   332
  35   59   91  131  179  235   299   371
  48   76  112  156  298  268   336   412
(row 1 of A000027) = (1,2,4,7,11,16,22,29,...), so (row 1 of B(1,2)) = (3,11,27,58,...);
(row 2 of A000027) = (3,5,8,12,17,23,30,38,...), so (row 2 of B(1,2)) = (8,20,40,68,...).

Cf. A000027, A163255, A333029, A361975 (array B(2,1)), A361976 (array B(2,2)).

zz = 10; z = 13;
w[n_, k_] := n + (n + k - 2) (n + k - 1)/2;
t[h_, k_] := w[h, 2 k - 1] + w[h, 2 k];
Table[t[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (*A361974 sequence*)
TableForm[Table[t[h, k], {h, 1, zz}, {k, 1, z}]] (*A361974 array*)

B(1,2) = (b(i,j)), where b(i,j) = w(i, 2j-1) + w(i, 2j) for i >= 1, j >= 1, where (w(i,j)) is the natural number array (A000027).

b(i,j) = 2i + (i + 2j - 2)^2.

A361976 (2,2)-block array, B(2,2), of the natural number array (A000027), read by descending antidiagonals.

Original entry on oeis.org

11, 31, 39, 67, 75, 83, 119, 127, 135, 143, 187, 195, 203, 211, 219, 271, 279, 287, 295, 303, 311, 371, 379, 387, 395, 403, 411, 419, 487, 495, 503, 511, 519, 527, 535, 543, 619, 627, 635, 643, 651, 659, 667, 675, 683, 767, 775, 783, 791, 799, 807, 815, 823

Offset: 1

Clark Kimberling, Apr 01 2023

We begin with a definition. Suppose that W = (w(i,j)), where i >= 1 and j >= 1, is an array of numbers such that if m and n satisfy 1 <= m < n, then there exists k such that w(m,k+h) < w(n,h+1) < w(m,k+h+1) for every h >= 0 . Then W is a row-splitting array. The array B(2,2) is a row-splitting array. The rows and columns of B(2,2) are linearly recurrent with signature (3,-3,1). It appears that the order array (as defined in A333029) of B(2,2) is given by A000027.

			Corner of B(2,2):
   11   31   67   119   187   271
   39   75  127   195   279   379
   83  135  203   287   387   503
  143  211  295   395   511   643
  219  303  403   519   651   799

Cf. A000027, A333029, A361974 (array B(1,2)), A361975 (array B(2,1)).

zz = 10; z = 13;
w[n_, k_] := n + (n + k - 2) (n + k - 1)/2;
t[n_, k_] := w[2 n - 1, 2 k - 1] + w[2 n - 1, 2 k] + w[2 n, 2 k - 1] + w[2 n, 2 k]
Table[t[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (*A361976 sequence*)
TableForm[Table[t[h, k], {h, 1, zz}, {k, 1, z}]] (*A361976 array*)

B(2,2) = (b(i,j)), where b(i,j) = w(2i-1,2j-1) + w(2i-1,2j) + w(2i,2j-1) + w(2i, 2j) for i >= 1, j >=1, where (w(i,j)) is the natural number array (A000027).

b(i,j) = 8(i+j)^2 - 12i - 20 j + 11.

A361994 (2,2)-block array, B(2,1), of the Wythoff array (A035513), read by descending antidiagonals.

Original entry on oeis.org

14, 37, 40, 97, 105, 69, 254, 275, 181, 95, 665, 720, 474, 249, 124, 1741, 1885, 1241, 652, 325, 150, 4558, 4935, 3249, 1707, 851, 393, 179, 11933, 12920, 8506, 4469, 2228, 1029, 469, 205, 31241, 33825, 22269, 11700, 5833, 2694, 1228, 537, 234, 81790, 88555

Offset: 1

Clark Kimberling, Apr 04 2023

We begin with a definition. Suppose that W = (w(i,j)), where i >= 1 and j >= 1, is an array of numbers such that if m and n satisfy 1 <= m < n, then there exists k such that w(m,k+h) < w(n,h+1) < w(m,k+h+1) for every h >= 0. Then W is a row-splitting array. The array B(2,2) is a row-splitting array. The rows of B(2,2) are linearly recurrent with signature (3,-1); the columns are linearly recurrent with signature (1,1,-1). The order array (as defined in A333029) of B(2,2) is A361996.

			Corner of B(2,2):
   14    37    97   254   665   1741 ...
   40   105   275   720  1885   4935 ...
   69   181   474  1241  3249   8506 ...
   95   249   652  1707  4469  11700 ...
  124   325   851  2228  5833  15271 ...
  ...
b(1,1) = w(1,1) + w(1,2) + w(2,1) + w(2,2) = 1 +  2 +  4 +  7 = 14;
b(1,2) = w(1,3) + w(1,4) + w(2,3) + w(2,4) = 3 +  5 + 11 + 18 = 37;
b(2,1) = w(3,1) + w(3,2) + w(4,1) + w(4,2) = 8 + 10 +  9 + 15 = 40.

Cf. A000045, A001622, A035513, A080164, A361976, A361992 (array B(1,2)), A361993 (array B(2,1)).

f[n_] := Fibonacci[n]; r = GoldenRatio;
zz = 10; z = 13;
w[n_, k_] := f[k + 1] Floor[n*r] + (n - 1) f[k]
t[h_, k_] := w[2 h - 1, 2 k - 1] + w[2 h - 1, 2 k] + w[2 h, 2 k - 1] + w[2 h, 2 k];
Table[t[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (*A361994 sequence *)
TableForm[Table[t[h, k], {h, 1, zz}, {k, 1, z}]] (* A361994 array *)

B(2,2) = (b(i,j)), where b(i,j) = w(2i-1,2j-1) + w(2i-1,2j) + w(2i,2j-1) + w(2i,2j) for i >= 1, j >= 1, where (w(i,j)) is the Wythoff array (A035513).

A361975 (2,1)-block array, B(2,1), of the natural number array (A000027), read by descending antidiagonals.

Original entry on oeis.org

4, 7, 16, 12, 23, 36, 19, 32, 47, 64, 28, 43, 60, 79, 100, 39, 56, 75, 96, 119, 144, 52, 71, 92, 115, 140, 167, 196, 67, 88, 111, 136, 163, 192, 223, 256, 84, 107, 132, 159, 188, 219, 252, 287, 324, 103, 128, 155, 184, 215, 248, 283, 320, 359, 400, 124, 151

Offset: 1

Clark Kimberling, Apr 01 2023

We begin with a definition. Suppose that W = (w(i,j)), where i >= 1 and j >= 1, is an array of numbers such that if m and n satisfy 1 <= m < n, then there exists k such that w(m,k+h) < w(n,h+1) < w(m,k+h+1) for every h >= 0. Then W is a row-splitting array. The array B(2,1) is a row-splitting array. The rows and columns of B(2,1) are linearly recurrent with signature (3,-3,1). It appears that the order array (as defined in A333029) of B(2,1) is given by A056537 (the dispersion of the nonsquares).

			Corner of B(2,1):
    4    7   12   19   28   39   52
   16   23   32   43   56   71   88
   36   47   60   75   92  111  132
   64   79   96  115  136  159  184
  100  119  140  163  188  215  244
  144  167  192  219  238  279  312
(column 1 of A000027) = (1,3,6,10,15,21,...), so (column 1 of B(2,1)) = (4,16,64,...);
(column 2 of A000027) = (2,5,9,14,20,27,...), so (column 2 of B(2,1)) = (7,23,47,...).

Cf. A000027, A056537, A333029, A361974 (array B(1,2)), A361976 (array B(2,2)).

zz = 10; z = 13;
w[n_, k_] := n + (n + k - 2) (n + k - 1)/2;
t[h_, k_] := w[2 h - 1, k] + w[2 h, k];
Table[t[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* this sequence *)
TableForm[Table[t[h, k], {h, 1, zz}, {k, 1, z}]] (* this sequence as an array *)

B(2,1) = (b(i,j)), where b(i,j) = w(2i-1, j) + w(2i, j) for i >= 1, j >= 1, where (w(i,j)) is the natural number array (A000027).

b(i,j) = 4i - 1 + (2i + j - 2)^2.

A361992 (1,2)-block array, B(1,2), of the Wythoff array (A035513), read by descending antidiagonals.

Original entry on oeis.org

3, 8, 11, 21, 29, 16, 55, 76, 42, 24, 144, 199, 110, 63, 32, 377, 521, 288, 165, 84, 37, 987, 1364, 754, 432, 220, 97, 45, 2584, 3571, 1974, 1131, 576, 254, 118, 50, 6765, 9349, 5168, 2961, 1508, 665, 309, 131, 58, 17711, 24476, 13530, 7752, 3948, 1741, 809

Offset: 1

Clark Kimberling, Apr 04 2023

We begin with a definition. Suppose that W = (w(i,j)), where i >= 1 and j >= 1, is an array of numbers such that if m and n satisfy 1 <= m < n, then there exists k such that w(m,k+h) < w(n,h+1) < w(m,k+h+1) for every h >= 0. Then W is a row-splitting array. The array B(1,2) is a row-splitting array. The rows of B(1,2) are linearly recurrent with signature (3,-1). The order array (as defined in A333029) of B(1,2) is the Wythoff difference array, A080164.

			Corner of B(1,2):
   3     8    21    55   144   377   987 ...
  11    29    76   199   521  1364  3571 ...
  16    42   110   288   754  1974  5168 ...
  24    63   165   432  1131  2961  7752 ...
  32    84   220   576  1508  3948 10336 ...
  ...
(row 1 of A035513) = (1,2,3,5,8,13,21,34,...), so (row 1 of B(1,2)) = (3,8,21,55,...);
(row 2 of A000027) = (4,7,11,18,29,47,76,123,...), so (row 2 of B(1,2)) = (11,29,76,199,...).

Cf. A000045, A001622, A035513, A080164, A361974, A361993 (array B(2,1)), A361994 (array B(2,2)).

f[n_] := Fibonacci[n]; r = GoldenRatio;
zz = 10; z = 13;
w[n_, k_] := f[k + 1] Floor[n*r] + (n - 1) f[k]
t[h_, k_] := w[h, 2 k - 1] + w[h, 2 k];
Table[t[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* A361992 sequence *)
TableForm[Table[t[h, k], {h, 1, zz}, {k, 1, z}]] (* A361992 array *)

B(1,2) = (b(i,j)), where b(i,j) = w(i, 2j-1) + w(i, 2j) for i >= 1, j >= 1, where (w(i,j)) is the Wythoff array (A035513).

b(i,j) = w(i,2j+1) = F(2 k + 2)*floor(h r) + (h - 1)F(2 k + 1), where F = A000045, the Fibonacci numbers, and r = (1+sqrt(5))/2, the golden ratio, A001622.

A361996 Order array of A361994, read by descending antidiagonals.

Original entry on oeis.org

1, 2, 3, 6, 7, 4, 15, 17, 11, 5, 39, 43, 28, 14, 8, 102, 112, 73, 38, 20, 9, 268, 292, 191, 100, 51, 23, 10, 568, 592, 491, 263, 132, 61, 27, 12, 868, 892, 791, 563, 345, 159, 72, 32, 13, 1168, 1192, 1091, 863, 645, 416, 189, 83, 35, 16, 1468, 1492, 1391

Offset: 1

Clark Kimberling, Apr 05 2023

This array is an interspersion (hence a dispersion, as in A114537 and A163255), so every positive integer occurs exactly once. See A333029 for the definition of order array.

			Corner:
  1    2    6   15   39  102  268 ...
  3    7   17   43  112  292  592 ...
  4   11   28   73  191  491  791 ...
  5   14   38  100  263  563  863 ...
  8   20   51  132  345  645  945 ...
  9   23   61  159  416  716 1016 ...
  ...

Cf. A114537, A163255, A333029, A361993, A361996.

zz = 300; z = 30;
w[n_, k_] := w[n, k] = Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
b[h_, k_] := b[h, k] = w[2 h - 1, 2 k - 1] + w[2 h - 1, 2 k] + w[2 h, 2 k - 1] + w[2 h, 2 k];
s = Flatten[Table[b[h, k], {h, 1, zz}, {k, 1, z}]];
r[h_, k_] := Length[Select[s, # <= b[h, k] &]]
TableForm[Table[r[h, k], {h, 1, 50}, {k, 1, 12}]](*A351996, array*)
v = Table[r[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (*A351996, sequence *)

A380649 Rectangular array ((-1)*D(i,j,1,2)) read by descending antidiagonals: D(i,j,s,n) denotes the determinant of the matrix described in Comments.

Original entry on oeis.org

1, 4, 3, 8, 7, 6, 13, 12, 11, 10, 19, 18, 17, 16, 15, 26, 25, 24, 23, 22, 21, 34, 33, 32, 31, 30, 29, 28, 43, 42, 41, 40, 39, 38, 37, 36, 53, 52, 51, 50, 49, 48, 47, 46, 45, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66

Offset: 1

Clark Kimberling, Jan 31 2025

Suppose that (m(i,j)) is a rectangular array of infinitely many rows and infinitely many columns. For integers s>=1 and n>=1, let M(i,j,s,n) be the nXn matrix (m(i+h*s,j+k*s)), where h=0..n-1, k=0..n-1.
Let D(i,j,s,n) and P(i,j,s,n) denote the determinant and permanent of M(i,j,s,n), respectively. For A380649, we take (m(i,j)) to be the natural number array (see A000027, A185787, and A144112), and ((-1)*D(i,j,1,2)) is as shown below in Example.
* D(i,j,1,1) = M(i,j,1,1) = m(i,j) has linearly recurrent row sequences, all with signature (3,-3,1).
* D(i,j,1,2) has linearly recurrent row sequences, all with signature (3,-3,1).
* (-1)*D(i,j,s,3) is the constant array in which every term is s^6, for all i,j,s.
* D(i,j,s,n) is the constant 0 array for all n>=4, for all i,j,s.
* P(i,j,s,n) depends only on n, and the rows all have the following linear recurrence signature:
b(2n+1,1), - b(2n+1,2), b(2n+1-3),..., -(2n+1,2n), 1, where b=binomial.
((-1)*D(i,j,1,2)) includes, exactly once, every positive integer not in A000096. The order array of ((-1)*D(i,j,1,2)) is the array in Example in A038722; see A333029 for the definition of order array.

			Corner of (-1)*D(i,j,1,2):
   1   4    8   13   19   26   34   43   53   64   76   89
   3   7   12   18   25   33   42   52   63   75   88  102
   6  11   17   24   32   41   51   62   74   87  101  116
  10  16   23   31   40   50   61   73   86  100  115  131
  15  22   30   39   49   60   72   85   99  114  130  147
  21  29   38   48   59   71   84   98  113  129  146  164
  28  37   47   58   70   83   97  112  128  145  163  182
  36  46   57   69   82   96  111  127  144  162  181  201
  45  56   68   81   95  110  126  143  161  180  200  221
  55  67   80   94  109  125  142  160  179  199  220  242
  66  79   93  108  124  141  159  178  198  219  241  264
  78  92  107  123  140  158  177  197  218  240  263  287
m(1,1) = 1, so M(1,1,1,2) is the matrix having (row 1) = (1,2) and (row 2) = (3,5), so (-1)*D(1,1,1,2) = -(1*5-2*3) = 1.

Cf. A000027, A000096, A038722, A185787, A333029, A380660, A380661.

s = 1; n = 2; z = 12;
r[n_, k_] := n + (n + k - 2)*(n + k - 1)/2;
Grid[Table[r[n, k], {n, 1, z}, {k, 1, z}]]  (* Array A000027 *)
FindLinearRecurrence[Table[r[1, k], {k, 1, 20}]]
t[i_, j_] := Table[r[i, j + k*s], {k, 0, n - 1}];
d[i_, j_] := -Det[Table[t[i + k*s, j], {k, 0, n - 1}]];  (* (-1)*D(i,j,s,n) *)
Grid[Table[d[i, j], {i, 1, z}, {j, 1, z}]]  (* array *)
FindLinearRecurrence[Table[d[12, k], {k, 1, 20}]]
Table[d[k, m - k], {m, 2, z}, {k, 1, m - 1}] // Flatten (* sequence *)

A340245 Order array of the Wythoff B-array (A340244): an interspersion, read by antidiagonals.

Original entry on oeis.org

1, 2, 4, 3, 7, 5, 6, 11, 9, 8, 10, 19, 15, 14, 12, 17, 31, 26, 23, 20, 13, 28, 51, 43, 39, 32, 22, 16, 46, 81, 71, 64, 53, 36, 27, 18, 75, 110, 101, 94, 83, 60, 44, 30, 21, 105, 138, 130, 123, 112, 90, 73, 49, 35, 24, 133, 165, 157, 151, 140, 119, 103, 79

Offset: 1

Clark Kimberling, Jan 02 2021

Suppose that (r(n,k)), for n >= 1 and k >= 1 is an array of distinct numbers. Replace each r(n,k) with its position when all the numbers r(n,k) are ordered by <. The resulting array is the order array of (r(n,k)). The order array A340245 is an interspersion and a dispersion, and, as a sequence, a permutation of the natural numbers; see A333029 and A191450.

			Corner:
   1    2    3    6   10    17    28    46
   4    7   11   19   31    51    81   110
   5    9   15   26   43    71   101   130
   8   14   23   39   64    94   123   151
  12   20   32   53   83   112   140   167

Cf. A191450, A333029, A340244.

r = GoldenRatio; f[n_] := Fibonacci[n];
a[n_] := Floor[r*n]; b[n_] := Floor[r^2*n];
c[n_] := a[a[b[n]]]; d[n_] := b[a[b[n]]];
w[n_, k_] := f[k - 2] c[n] + f[k - 1] d[n];
Grid[Table[w[n, k], {n, 1, 9}, {k, 1, 15}]] (* A340244 array *)
u = Table[w[n - k + 1, k], {n, 30}, {k, n, 1, -1}]//Flatten  (* A340244 sequence *)
rk[n_] := Position[Sort[u], u[[n]]];
Take[Flatten[Table[rk[n], {n, 1, 350}]], 100]  (* A340245 sequence *)

cp's OEIS Frontend

A361993 (2,1)-block array, B(2,1), of the Wythoff array (A035513), read by descending antidiagonals.

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A333028 Array consisting of the primitive rows of the Wythoff array (A035513), read by antidiagonals.

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A361974 (1,2)-block array, B(1,2), of the natural number array (A000027), read by descending antidiagonals.

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A361976 (2,2)-block array, B(2,2), of the natural number array (A000027), read by descending antidiagonals.

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A361994 (2,2)-block array, B(2,1), of the Wythoff array (A035513), read by descending antidiagonals.

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A361975 (2,1)-block array, B(2,1), of the natural number array (A000027), read by descending antidiagonals.

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A361992 (1,2)-block array, B(1,2), of the Wythoff array (A035513), read by descending antidiagonals.

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A361996 Order array of A361994, read by descending antidiagonals.

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A380649 Rectangular array ((-1)*D(i,j,1,2)) read by descending antidiagonals: D(i,j,s,n) denotes the determinant of the matrix described in Comments.