A211422 -id:A211422 - cp's OEIS frontend

A211647 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2+x^2+y^2<=3n.

0, 1, 4, 7, 11, 17, 23, 32, 38, 48, 60, 66, 78, 87, 102, 114, 121, 139, 157, 169, 178, 196, 214, 232, 241, 263, 284, 296, 314, 329, 359, 371, 386, 410, 434, 452, 471, 495, 516, 540, 555, 582, 612, 630, 651, 678, 702, 729, 738, 772, 805, 829, 853, 871

Offset: 0

Clark Kimberling, Apr 18 2012

nonn

For a guide to related sequences, see A211422.

Cf. A211422.

t = Compile[{{n, _Integer}}, Module[{s = 0},
    (Do[If[w^2 + x^2 + y^2 <= 3 n, s = s + 1],
        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 80]]  (* A211647 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A211648 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2+x^2+y^2=3n.

Original entry on oeis.org

0, 1, 3, 3, 1, 0, 3, 6, 3, 4, 6, 6, 3, 0, 6, 6, 1, 6, 12, 6, 0, 0, 12, 12, 3, 7, 6, 12, 6, 0, 12, 6, 3, 9, 6, 12, 4, 0, 12, 12, 6, 6, 18, 18, 6, 0, 12, 12, 3, 7, 15, 15, 0, 0, 12, 12, 6, 15, 18, 6, 6, 0, 18, 24, 1, 12, 15, 18, 6, 0, 12, 12, 12, 12, 18, 15, 6, 0, 24, 18, 0, 13, 18

Offset: 0

Clark Kimberling, Apr 18 2012

nonn

For a guide to related sequences, see A211422.

Cf. A211422.

t = Compile[{{n, _Integer}}, Module[{s = 0},
    (Do[If[w^2 + x^2 + y^2 == 3 n, s = s + 1],
        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 100]]  (* A211648 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A211652 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^4

Original entry on oeis.org

0, 1, 7, 22, 50, 95, 161, 253, 374, 528, 721, 955, 1236, 1567, 1953, 2396, 2902, 3475, 4117, 4837, 5634, 6516, 7485, 8545, 9700, 10956, 12316, 13783, 15365, 17062, 18880, 20821, 22892, 25096, 27437, 29921, 32548, 35324, 38256, 41345

Offset: 0

Clark Kimberling, Apr 19 2012

nonn

For a guide to related sequences, see A211422.

Cf. A211422.

t = Compile[{{n, _Integer}}, Module[{s = 0},
    (Do[If[w^4 < x^4 + y^4, s = s + 1],
        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A211652 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A211653 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^4>x^4+y^4.

Original entry on oeis.org

0, 0, 1, 5, 14, 30, 55, 90, 138, 201, 279, 376, 492, 630, 791, 979, 1194, 1438, 1715, 2022, 2366, 2745, 3163, 3622, 4124, 4669, 5260, 5900, 6587, 7327, 8120, 8970, 9876, 10841, 11867, 12954, 14108, 15329, 16616, 17974, 19405, 20907, 22486

Offset: 0

Clark Kimberling, Apr 19 2012

nonn

For a guide to related sequences, see A211422.

Cf. A211422.

t = Compile[{{n, _Integer}}, Module[{s = 0},
    (Do[If[w^4 > x^4 + y^4, s = s + 1],
        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]    (* A211653 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A182195 Numbers k for which no numbers w,x,y, all in {1,...,k}, satisfy w^2 + x^2 + y^2 = 2k.

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 10, 14, 16, 20, 26, 29, 30, 32, 40, 46, 50, 56, 62, 64, 65, 74, 78, 80, 94, 104, 110, 116, 120, 126, 128, 142, 158, 160, 170, 174, 184, 190, 200, 206, 222, 224, 238, 248, 254, 256, 260, 270, 286, 296, 302, 312, 318, 320, 334, 350, 366

Offset: 0

Clark Kimberling, Apr 18 2012

nonn

For a guide to related sequences, see A211422.

Cf. A211422.

t = Compile[{{n, _Integer}}, Module[{s = 0},
    (Do[If[w^2 + x^2 + y^2 == 2 n, s = s + 1],
        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 400]]    (* A211649 *)
-1 + Flatten[Position[%, 0]]  (* this sequence *)
(* Peter J. C. Moses, Apr 13 2012 *)

cp's OEIS Frontend

A211647 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2+x^2+y^2<=3n.

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A211648 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2+x^2+y^2=3n.

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A211652 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^4

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Author

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Comments

Crossrefs

Programs

Mathematica

A211653 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^4>x^4+y^4.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A182195 Numbers k for which no numbers w,x,y, all in {1,...,k}, satisfy w^2 + x^2 + y^2 = 2k.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica