A211790 -id:A211790 - cp's OEIS frontend

A211800 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2*w^2 < x^2 + y^2.

0, 3, 13, 32, 64, 113, 181, 272, 388, 535, 713, 926, 1180, 1475, 1815, 2204, 2646, 3141, 3695, 4312, 4992, 5741, 6563, 7460, 8432, 9485, 10625, 11850, 13166, 14579, 16089, 17696, 19410, 21233, 23161, 25204, 27366, 29647, 32051, 34580

Offset: 1

Clark Kimberling, Apr 22 2012

nonn

Row 2 of A211802; see A211790 for a discussion and guide to related sequences.

Cf. A211790, A211801, A211802.

Mathematica
```
(See the program at A211802.)
```

Definition corrected by Georg Fischer, Sep 10 2022

A211803 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^2>=x^2+y^2.

Original entry on oeis.org

1, 5, 14, 32, 61, 103, 162, 240, 341, 465, 618, 802, 1017, 1269, 1560, 1892, 2267, 2691, 3164, 3688, 4269, 4907, 5604, 6364, 7193, 8091, 9058, 10102, 11223, 12421, 13702, 15072, 16527, 18071, 19714, 21452, 23287, 25225, 27268, 29420

Offset: 1

Clark Kimberling, Apr 22 2012

nonn

Row 2 of A211805; see A211790 for a discussion and guide to related sequences.

Cf. A211790, A211805.

Mathematica
```
(See the program at A211805.)
```

A211804 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^3>=x^3+y^3.

Original entry on oeis.org

1, 5, 14, 30, 57, 99, 156, 230, 323, 441, 588, 762, 965, 1199, 1476, 1792, 2149, 2547, 2990, 3488, 4039, 4643, 5300, 6012, 6797, 7645, 8558, 9540, 10591, 11729, 12944, 14236, 15607, 17065, 18620, 20262, 21993, 23817, 25746, 27778, 29915

Offset: 1

Clark Kimberling, Apr 22 2012

nonn

Row 3 of A211805; see A211790 for a discussion and guide to related sequences.

Cf. A211790, A211805.

Mathematica
```
(See the program at A211805.)
```

A211806 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^2<=x^2+y^2.

Original entry on oeis.org

1, 5, 16, 36, 69, 119, 190, 282, 399, 547, 726, 940, 1195, 1493, 1834, 2224, 2669, 3165, 3720, 4338, 5021, 5771, 6596, 7494, 8467, 9521, 10662, 11890, 13207, 14621, 16134, 17742, 19457, 21283, 23214, 25258, 27421, 29703, 32108, 34638

Offset: 1

Clark Kimberling, Apr 22 2012

nonn

Row 2 of A211808; see A211790 for a discussion and guide to related sequences.

Cf. A211790, A211808.

Mathematica
```
(See the program at A211808.)
```

A211810 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^2>x^2+y^2.

Original entry on oeis.org

0, 3, 11, 28, 56, 97, 153, 230, 330, 453, 605, 788, 1002, 1251, 1541, 1872, 2244, 2667, 3139, 3662, 4240, 4877, 5571, 6330, 7158, 8055, 9021, 10062, 11182, 12379, 13657, 15026, 16480, 18021, 19661, 21398, 23232, 25169, 27211, 29362, 31618

Offset: 1

Clark Kimberling, Apr 22 2012

nonn

Row 2 of A182259; see A211790 for a discussion and guide to related sequences.

Cf. A211790, A182259.

Mathematica
```
(See the program at A182259.)
```

A211811 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^3>x^3+y^3.

Original entry on oeis.org

0, 3, 11, 26, 52, 93, 149, 222, 314, 431, 577, 750, 952, 1185, 1461, 1776, 2132, 2529, 2971, 3468, 4018, 4621, 5277, 5988, 6772, 7619, 8531, 9512, 10562, 11699, 12913, 14204, 15574, 17031, 18585, 20226, 21956, 23779, 25707, 27738, 29874

Offset: 1

Clark Kimberling, Apr 22 2012

nonn

Row 3 of A182259; see A211790 for a discussion and guide to related sequences.

Cf. A211790, A182259.

Mathematica
```
(See the program at A182259.)
```

A211793 Rectangular array: R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and w^k >= x^k + y^k.

Original entry on oeis.org

0, 1, 0, 4, 1, 0, 10, 5, 1, 0, 20, 13, 5, 1, 0, 35, 28, 14, 5, 1, 0, 56, 50, 29, 14, 5, 1, 0, 84, 80, 53, 30, 14, 5, 1, 0, 120, 121, 88, 55, 30, 14, 5, 1, 0, 165, 175, 134, 90, 55, 30, 14, 5, 1, 0, 220, 244, 195, 138, 91, 55, 30, 14, 5, 1, 0, 286, 327, 270, 201, 139

Offset: 1

Clark Kimberling, Apr 21 2012

Limiting row sequence: A000330.

			Northwest corner:
  0, 1, 4, 10, 20, 35, 56,  84
  0, 1, 5, 13, 28, 50, 80, 121
  0, 1, 5, 14, 29, 53, 88, 134
  0, 1, 5, 14, 30, 55, 90, 138
  0, 1, 5, 14, 30, 55, 91, 139
  0, 1, 5, 14, 30, 55, 91, 140

Cf. A211790.

Cf. A000292 (row 1), A211636 (row 2), A211651 (row 3), A000330.

z = 48;
t[k_, n_] := Module[{s = 0},
   (Do[If[w^k >= x^k + y^k, s = s + 1],
       {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
Table[t[1, n], {n, 1, z}]  (* A000292 *)
Table[t[2, n], {n, 1, z}]  (* A211636 *)
Table[t[3, n], {n, 1, z}]  (* A211651 *)
TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* this sequence *)
Table[k (k - 1) (2 k - 1)/6, {k, 1,
  z}] (* row-limit sequence, A000330 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A211790(k,n) + R(k,n) = 3^(n-1).

cp's OEIS Frontend

A211800 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2*w^2 < x^2 + y^2.

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A211803 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^2>=x^2+y^2.

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A211804 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^3>=x^3+y^3.

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Mathematica

A211806 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^2<=x^2+y^2.

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Mathematica

A211810 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^2>x^2+y^2.

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Mathematica

A211811 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^3>x^3+y^3.

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Programs

Mathematica

A211793 Rectangular array: R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and w^k >= x^k + y^k.

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