A216226 -id:A216226 - cp's OEIS frontend

A216230 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=2, T(0,0) = T(0,1) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 14 2013

			Square array begins:
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, ...
...

Cf. A000012, A068914

Cf. Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229

T(n,n) = T(n,n+1) = 1.

Sum_{k, 0<=k<=n} T(n-k, k) = 1.

A223968 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 5 or if k-n >= 6, T(4,0) = T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 0, 0, 6, 15, 20, 15, 5, 0, 0, 6, 21, 35, 35, 20, 0, 0, 0, 0, 27, 56, 70, 55, 20, 0, 0, 0, 0, 27, 83, 126, 125, 75, 0, 0, 0, 0, 0, 0, 110, 209, 251, 200, 75, 0, 0, 0, 0, 0, 0, 110, 319, 460, 451, 275, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 30 2013

			Square array begins:
1....1....1....1....1....1....0....0....0....0....0....0
1....2....3....4....5....6....6....0....0....0....0....0
1....3....6...10...15...21...27...27....0....0....0....0
1....4...10...20...35...56...83..110..110....0....0....0
1....5...15...35...70..126..209..319..429..429....0....0
0....5...20...55..125..251..460..779.1208.1637.1637....0
0....0...20...75..200..451..911.1690.2898.4535.6172.6172
...
Square array, read by diagonals, with 0 omitted:
1, 5, 20, 75, 275, 1001, 3639, 13243, 48280, ...
1, 5, 20, 75, 275, 1001, 3639, 13243, 48280, ...
1, 4, 15, 55, 200, 726, 2638, 9604, 35037, ...
1, 3, 10, 35, 125, 451, 1637, 5965, 21794, ...
1, 2, 6, 20, 70, 251, 911, 3327, 12190, 44744, ...
1, 3, 10, 35, 126, 460, 1690, 6225, 22950, ...
1, 4, 15, 56, 209, 779, 2898, 10760, 39882, ...
1, 5, 21, 83, 319, 1208, 4535, 16932, 62986, ...
1, 6, 27, 110, 429, 1637, 6172, 23104, 86090, ...
1, 6, 27, 110, 429, 1637, 6172, 23104, 86090, ...

sum(T(n-k,k), 0<=k<=n) = A223940(n).
T(n,n+5) = T(n,n+4) = A221863(n).
T(n,n+3) = A221862(n).
T(n,n+2) = A221859(n).
T(n,n+1) = A216710(n).
T(n,n) = A224514(n).
T(n+1,n) = A224509(n).
T(n+2,n) = A220948(n).
T(n+3,n) = T(n+4,n) = A224422(n). - Philippe Deléham, Apr 13 2013

A216229 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=3, T(1,0) = T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 1, 1, 2, 0, 0, 3, 2, 0, 0, 3, 5, 0, 0, 0, 0, 8, 5, 0, 0, 0, 0, 8, 13, 0, 0, 0, 0, 0, 0, 21, 13, 0, 0, 0, 0, 0, 0, 21, 34, 0, 0, 0, 0, 0, 0, 0, 0, 55, 34, 0, 0, 0, 0, 0, 0, 0, 0, 55, 89, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 14 2013

			Square array begins:
1, 1, 1,  0,  0,  0,   0,   0, ... row n=0
1, 2, 3,  3,  0,  0,   0,   0, ... row n=1
0, 2, 5,  8,  8,  0,   0,   0, ... row n=2
0, 0, 5, 13, 21, 21,   0,   0, ... row n=3
0, 0, 0, 13, 34, 55,  55,   0, ... row n=4
0, 0, 0,  0, 34, 89, 144, 144, ... row n=5
...

Cf. A000045 (Fibonacci numbers), A001519, A001906, A216226

T(n,n) = T(n+1,n) = A001519(n+1).
T(n,n+1) = T(n,n+2) = A001906(n+1).
Sum_{k, 0<=k<=n} T(n-k,k) = A000045(n+2).
T(n,k) = A216226(n,k+1).

A216232 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 3 or if k-n >= 5, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 3, 0, 1, 4, 6, 3, 0, 0, 5, 10, 9, 0, 0, 0, 5, 15, 19, 9, 0, 0, 0, 0, 20, 34, 28, 0, 0, 0, 0, 0, 20, 54, 62, 28, 0, 0, 0, 0, 0, 0, 74, 116, 90, 0, 0, 0, 0, 0, 0, 0, 74, 190, 206, 90, 0, 0, 0, 0, 0, 0, 0, 0, 264, 396, 296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 660, 692, 296, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 14 2013

Arithmetic hexagon of E. Lucas.

			Square array begins:
  1, 1, 1,  1,  1,   0,   0,   0,   0,   0, 0, ... row n=0
  1, 2, 3,  4,  5,   5,   0,   0,   0,   0, 0, ... row n=1
  1, 3, 6, 10, 15,  20,  20,   0,   0,   0, 0, ... row n=2
  0, 3, 9, 19, 34,  54,  74,  74,   0,   0, 0, ... row n=3
  0, 0, 9, 28, 62, 116, 190, 264, 264,   0, 0, ... row n=4
  0, 0, 0, 28, 90, 206, 396, 660, 924, 924, 0, ... row n=5
  ...
Array, read by rows, with 0 omitted:
   1,   1,   1,   1,    1
   1,   2,   3,   4,    5,    5
   1,   3,   6,  10,   15,   20,   20
        3,   9,  19,   34,   54,   74,   74
             9,  28,   62,  116,  190,  264,  264
                 28,   90,  206,  396,  660,  924,  924
                       90,  296,  692, 1352, 2276, 3200, 3200
  ...

E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome 1, p. 89.

E. Lucas, Théorie des nombres, Gauthier-Villars, Paris 1891, Tome 1, p. 89.

Cf. A007052, A094803, A094806, A094817, A094821

Cf. similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230.

T(n,n) = A094817(n), for n > 0.
T(n+1,n) = T(n+2,n) = A094803(n).
T(n,n+1) = A007052(n).
T(n,n+2) = A094821(n+1).
T(n,n+3) = T(n,n+4) = A094806(n).
Sum_{k=0..n} T(n-k,k) = A217730(n). - Philippe Deléham, Mar 22 2013

A217770 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=4 or if k-n >= 6, T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 0, 1, 5, 10, 10, 4, 0, 0, 6, 15, 20, 14, 0, 0, 0, 6, 21, 35, 34, 14, 0, 0, 0, 0, 27, 56, 69, 48, 0, 0, 0, 0, 0, 27, 83, 125, 117, 48, 0, 0, 0, 0, 0, 0, 110, 208, 242, 165, 0, 0, 0, 0, 0, 0, 0, 110, 318, 450, 407, 165

Offset: 0

Philippe Deléham, Mar 24 2013

A hexagon arithmetic of E. Lucas.

			Square array begins:
n=0: 1, 1,  1,  1,   1,   1,   0,   0,    0,    0,    0, 0, ...
n=1: 1, 2,  3,  4,   5,   6,   6,   0,    0,    0,    0, 0, ...
n=2: 1, 3,  6, 10,  15,  21,  27,  27,    0,    0,    0, 0, ...
n=3: 1, 4, 10, 20,  35,  56,  83, 110,  110,    0,    0, 0, ...
n=4: 0, 4, 14, 34,  69, 125, 208, 318,  428,  428,    0, 0, ...
n=5: 0, 0, 14, 48, 117, 242, 450, 768, 1196, 1624, 1624, 0, ...
...
Square array, read by rows, with 0 omitted:
...1,    1,     1,     1,     1,      1
...1,    2,     3,     4,     5,      6,      6
...1,    3,     6,    10,    15,     21,     27,     27
...1,    4,    10,    20,    35,     56,     83,    110,    110
...4,   14,    34,    69,   125,    208,    318,    428,    428
..14,   48,   117,   242,   450,    768,   1196,   1624,   1624
..48,  165,   407,   857,  1625,   2821,   4445,   6069,   6069
.165,  572,  1429,  3054,  5875,  10320,  16389,  22458,  22458
.572, 2001,  5055, 10930, 21250,  37639,  60097,  82555,  82555
2001, 7056, 17986, 39236, 76875, 136972, 219527, 302082, 302082
...
Triangle begins:
1
1, 1
1, 2,  1
1, 3,  3,  1
1, 4,  6,  4,  0
1, 5, 10, 10,  4,  0
0, 6, 15, 20, 14,  0, 0
0, 6, 21, 35, 34, 14, 0, 0
...

Cf. Similar sequences: A214846, A216054, A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236, A216238, A217257, A217315, A217593, A217765.

T(n,n+4) = T(n,n+5) = A094788(n+2).
T(n,n+3) = A217783(n).
T(n,n+2) = A217779(n).
T(n,n+1) = A081567(n).
T(n,n)   = A217782(n).
T(n+1,n) = A217778(n).
T(n+3,n) = T(n+2,n) = A094667(n+1).
Sum(T(n-k,k), k=0..n) = A217777(n).

A216238 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=5, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 0, 4, 5, 0, 0, 0, 0, 4, 9, 5, 0, 0, 0, 0, 0, 13, 14, 0, 0, 0, 0, 0, 0, 13, 27, 14, 0, 0, 0, 0, 0, 0, 0, 40, 41, 0, 0, 0, 0, 0, 0, 0, 0, 40, 81, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121, 122, 0, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 14 2013

Hexagon arithmetic of E. Lucas.

			Square array begins:
1, 1, 1, 1,  1,  0,   0,   0,   0,    0,    0, ... row n=0
0, 1, 2, 3,  4,  4,   0,   0,   0,    0,    0, ... row n=1
0, 0, 2, 5,  9, 13,  13,   0,   0,    0,    0, ... row n=2
0, 0, 0, 5, 14, 27,  40,  40,   0,    0,    0, ... row n=3
0, 0, 0, 0, 14, 41,  81, 121, 121,    0,    0, ... row n=4
0, 0, 0, 0,  0, 41, 122, 243, 364,  364,    0, ... row n=5
0, 0, 0, 0,  0,  0, 122, 365, 729, 1093, 1093, ... row n=6
...

E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome1, p.89

E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, 1991, p.89

Cf. A000244, A003462, A124302, A182522.

Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236.

T(n,n) = A124302(n).
T(n,n+1) = A124302(n+1).
T(n,n+2) = 3^n = A000244(n).
T(n,n+3) = T(n,n+4) = A003462(n+1).
Sum_{k, 0<=k<=n} T(n-k,k) = A182522(n).

A216054 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 6, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 5, 0, 0, 0, 0, 5, 9, 5, 0, 0, 0, 0, 5, 14, 14, 0, 0, 0, 0, 0, 0, 19, 28, 14, 0, 0, 0, 0, 0, 0, 19, 47, 42, 0, 0, 0, 0, 0, 0, 0, 0, 66, 89, 42, 0, 0, 0, 0, 0, 0, 0, 0, 66, 155, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 221, 286, 131, 0, 0

Offset: 0

Philippe Deléham, Mar 16 2013

A hexagon arithmetic of E. Lucas.

			Square array begins:
1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=0
0, 1, 2, 3, 4, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=1
0, 0, 2, 5, 9, 14, 19, 19, 0, 0, 0, 0, 0, 0, 0, ... row n=2
0, 0, 0, 5, 14, 28, 47, 66, 66, 0, 0, 0, 0, 0, 0, ... row n=3
0, 0, 0, 0, 14, 42, 89, 155, 221, 221, 0, 0, 0, 0, ... row n=4
0, 0, 0, 0, 0, 0, 42, 131, 286, 507, 728, 728, 0, 0, ... row n=5
0, 0, 0, 0, 0, 0, 131, 417, 924, 1652, 2380, 2380, 0, ... row n=6
...

E. Lucas, Théorie des nombres, A.Blanchard, Paris, 1958, Tome 1, p.89

Cf. A006053, A052547, A096976, A187066,

Cf. Similar sequences A216230, A216228, A216226, A216238

Clear[t]; t[0, k_ /; k <= 5] = 1; t[n_, k_] /; k < n || k > n+5 = 0; t[n_, k_] := t[n, k] = t[n-1, k] + t[n, k-1]; Table[t[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 18 2013 *)

T(n,n) = A080937(n).
T(n,n+1) = A080937(n+1).
T(n,n+2) = A094790(n+1).
T(n,n+3) = A094789(n+1).
T(n,n4) = T(n,n+5) = A005021(n).
Sum_{k, 0<=k<=n} T(n-k,k) = A028495(n).

A216235 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 2 or if k-n >= 5, T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 1, 1, 2, 0, 1, 3, 2, 0, 1, 4, 5, 0, 0, 0, 5, 9, 5, 0, 0, 0, 5, 14, 14, 0, 0, 0, 0, 0, 19, 28, 14, 0, 0, 0, 0, 0, 19, 47, 42, 0, 0, 0, 0, 0, 0, 0, 66, 89, 42, 0, 0, 0, 0, 0, 0, 0, 66, 155, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 221, 286, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 221, 507, 417, 0, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 14 2013

Arithmetic hexagon of E. Lucas.

			Square array begins:
  1, 1, 1,  1,  1,   0,   0,   0,   0,   0, ... row n=0
  1, 2, 3,  4,  5,   5,   0,   0,   0,   0, ... row n=1
  0, 2, 5,  9, 14,  19,  19,   0,   0,   0, ... row n=2
  0, 0, 5, 14, 28,  47,  66,  66,   0,   0, ... row n=3
  0, 0, 0, 14, 42,  89, 155, 221, 221,   0, ... row n=4
  0, 0, 0,  0, 42, 131, 286, 507, 728, 728, ... row n=5
  ...

E. Lucas, Théorie des nombres, Gauthier-Villars, Paris 1891, Tome 1, p. 89.

Cf. A005021, A080937, A094789, A094790.

Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232.

T(n,n) = T(n+1,n) = A080937(n+1).
T(n,n+1) = A094790(n+1).
T(n,n+2) = A094789(n+1).
T(n,n+3) = T(n,n+4) = A005021(n).
Sum_{k=0..n} T(n-k,k) = A028495(n+1). - Philippe Deléham, Mar 23 2013

A216236 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=4 or if k-n>=5, T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 0, 0, 5, 10, 10, 4, 0, 0, 5, 15, 20, 14, 0, 0, 0, 0, 20, 35, 34, 14, 0, 0, 0, 0, 20, 55, 69, 48, 0, 0, 0, 0, 0, 0, 75, 124, 117, 48, 0, 0, 0, 0, 0, 0, 75, 199, 241, 165, 0, 0, 0, 0, 0, 0, 0, 0, 274, 440, 406, 165, 0, 0, 0, 0, 0, 0, 0, 0, 274, 714, 846, 571, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 14 2013

Arithmetic hexagon of E. Lucas.

			Square array begins:
1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...
1, 2, 3, 4, 5, 5, 0, 0, 0, 0, 0, ...
1, 3, 6, 10, 15, 20, 20, 0, 0, 0, ...
1, 4, 10, 20, 35, 55, 75, 75, 0, 0, 0, ...
0, 4, 14, 34, 69, 124, 199, 274, 274, 0, 0, ...
0, 0, 14, 48, 117, 241, 440, 714, 988, 988, 0, ...
...

E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome 1, p. 89

E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, 1991, p.89

Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235.

T(n+3,n) = T(n+2,n) = A094827(n).
T(n+1,n) = A094832(n).
T(n,n) = A094854(n).
T(n,n+1) = A094855(n).
T(n,n+2) = A094833(n+1).
T(n,n+3) = T(n,n+4) = A094828(n).
Sum( T(n-k,k), 0<=k<=n ) = A217733(n). - Philippe Deléham, Mar 22 2013

A217257 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 7, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,3) = T(0,4) = T(0,5) = T(0,6) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 5, 0, 0, 0, 1, 5, 9, 5, 0, 0, 0, 0, 6, 14, 14, 0, 0, 0, 0, 0, 6, 20, 28, 14, 0, 0, 0, 0, 0, 0, 26, 48, 42, 0, 0, 0, 0, 0, 0, 0, 26, 74, 90, 42, 0, 0, 0, 0, 0, 0, 0, 0, 100, 164, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 264, 296, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364, 560, 428, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Philippe Deléham, Mar 17 2013

A hexagon arithmetic of E. Lucas.

			Square array begins:
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=0
0, 1, 2, 3, 4, 5, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=1
0, 0, 2, 5, 9, 14, 20, 26, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=2
0, 0, 0, 5, 14, 28, 48, 74, 100, 100, 0, 0, 0, 0, 0, 0, 0, ... row n=3
0, 0, 0, 0, 14, 42, 90, 162, 264, 364, 364, 0, 0, 0, 0, 0, ... row n=4
0, 0, 0, 0, 0, 42, 132, 296, 560, 924, 1288, 1288, 0, 0, 0, ... row n=5
...

E. Lucas, Théorie des nombres, A. Blanchard, Paris, 1958, p.89

E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, p. 89

Cf. similar sequences: A216230, A216228, A216226, A216238, A216054.

T(n,n) = A024175(n).
T(n,n+1) = A024175(n+1).
T(n,n+2) = A094803(n+1).
T(n,n+3) = A007070(n).
T(n,n+4) = A094806(n+2).
T(n,n+5) = T(n,n+6) = A094811(n+2).
Sum_{k, 0<=k<=n} T(n-k,k) = A030436(n).

a(69) = 0 deleted by Georg Fischer, Oct 16 2021

cp's OEIS Frontend

A216230 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=2, T(0,0) = T(0,1) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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A223968 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 5 or if k-n >= 6, T(4,0) = T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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A216229 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=3, T(1,0) = T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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A216232 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 3 or if k-n >= 5, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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A217770 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=4 or if k-n >= 6, T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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A216238 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=5, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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A216054 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 6, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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A216235 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 2 or if k-n >= 5, T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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A216236 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=4 or if k-n>=5, T(3,0) = T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

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