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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A211923 Number of (w,x,y,z) with all terms in {1,...,n} and 2*w*x>=3*y*z.

Original entry on oeis.org

0, 0, 5, 31, 96, 238, 504, 921, 1585, 2560, 3896, 5698, 8113, 11165, 15042, 19860, 25733, 32814, 41320, 51271, 63015, 76686, 92385, 110397, 131022, 154298, 180579, 210119, 243109, 279810, 320658, 365615, 415291, 469881, 529582, 594834, 666111, 743335, 827162
Offset: 0

Views

Author

Clark Kimberling, Apr 28 2012

Keywords

Comments

a(n)+A211920(n)=n^4.
See A211795 for a guide to related sequences.

Crossrefs

Cf. A211795.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[2 w*x >= 3 y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A211923 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A212053 Number of (w,x,y,z) with all terms in {1,...,n} and w*x<=y*z+1.

Original entry on oeis.org

0, 1, 13, 56, 158, 365, 725, 1312, 2198, 3477, 5245, 7624, 10742, 14725, 19725, 25920, 33470, 42557, 53397, 66176, 81150, 98525, 118533, 141456, 167606, 197189, 230509, 267920, 309726, 356205, 407805, 464744, 527494, 596389, 671789
Offset: 0

Views

Author

Clark Kimberling, Apr 29 2012

Keywords

Comments

a(n)+A212054(n)=n^4. See A211795 for a guide to related sequences.

Crossrefs

Cf. A211795.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*x <= y*z + 1, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212053 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A212054 Number of (w,x,y,z) with all terms in {1,...,n} and w*x>y*z+1.

Original entry on oeis.org

0, 0, 3, 25, 98, 260, 571, 1089, 1898, 3084, 4755, 7017, 9994, 13836, 18691, 24705, 32066, 40964, 51579, 64145, 78850, 95956, 115723, 138385, 164170, 193436, 226467, 263521, 304930, 351076, 402195, 458777, 521082, 589532, 664547
Offset: 0

Views

Author

Clark Kimberling, Apr 29 2012

Keywords

Comments

a(n)+A212053(n)=n^4. See A211795 for a guide to related sequences.

Crossrefs

Cf. A211795.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*x > y*z + 1, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212054 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A212056 Number of (w,x,y,z) with all terms in {1,...,n} and w*x>y*z+2.

Original entry on oeis.org

0, 0, 1, 19, 80, 230, 521, 1019, 1800, 2966, 4593, 6819, 9768, 13566, 18353, 24339, 31640, 40478, 51025, 63523, 78168, 95230, 114881, 137459, 163184, 192374, 225265, 262251, 303568, 349606, 400633, 457099, 519280, 587654, 662481
Offset: 0

Views

Author

Clark Kimberling, Apr 29 2012

Keywords

Comments

a(n)+A212056(n)=n^4. See A211795 for a guide to related sequences.

Crossrefs

Cf. A211795.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*x > y*z + 2, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212056 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A212057 Number of (w,x,y,z) with all terms in {1,...,n} and w

Original entry on oeis.org

0, 0, 11, 69, 231, 584, 1230, 2307, 3964, 6385, 9771, 14356, 20377, 28125, 37894, 50008, 64809, 82681, 104005, 129216, 158743, 193063, 232668, 278080, 329812, 388452, 454585, 528822, 611791, 704167, 806610, 919852, 1044607, 1181643
Offset: 0

Views

Author

Clark Kimberling, Apr 30 2012

Keywords

Comments

a(n)+A212058(n)=n^4. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795, A061201.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w < x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212057 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A212058 Number of (w,x,y,z) with all terms in {1,...,n} and w>=x*y*z.

Original entry on oeis.org

0, 1, 5, 12, 25, 41, 66, 94, 132, 176, 229, 285, 359, 436, 522, 617, 727, 840, 971, 1105, 1257, 1418, 1588, 1761, 1964, 2173, 2391, 2619, 2865, 3114, 3390, 3669, 3969, 4278, 4596, 4923, 5286, 5652, 6027, 6411, 6825, 7242, 7686, 8133, 8598
Offset: 0

Views

Author

Clark Kimberling, Apr 30 2012

Keywords

Comments

a(n)+A212057(n)=n^4. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795, A061201.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w >= x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212058 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Formula

a(n) = Sum_{i=1..n+1} Sum_{j=1..n+1} tau(i)*floor((n+1-j)/i). - Ridouane Oudra, Oct 03 2020

A212063 Number of (w,x,y,z) with all terms in {1,...,n} and w^2

Original entry on oeis.org

0, 0, 8, 50, 169, 440, 943, 1796, 3118, 5090, 7877, 11683, 16708, 23253, 31552, 41892, 54589, 70030, 88524, 110484, 136289, 166434, 201327, 241465, 287278, 339444, 398407, 464742, 539068, 622021, 714192, 816319, 929007, 1053100
Offset: 0

Views

Author

Clark Kimberling, Apr 30 2012

Keywords

Comments

a(n)+A212064(n)=n^4. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^2 < x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212063 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A212064 Number of (w,x,y,z) with all terms in {1,...,n} and w^2>=x*y*z.

Original entry on oeis.org

0, 1, 8, 31, 87, 185, 353, 605, 978, 1471, 2123, 2958, 4028, 5308, 6864, 8733, 10947, 13491, 16452, 19837, 23711, 28047, 32929, 38376, 44498, 51181, 58569, 66699, 75588, 85260, 95808, 107202, 119569, 132821, 147102, 162427, 178898
Offset: 0

Views

Author

Clark Kimberling, Apr 30 2012

Keywords

Comments

a(n)+A212063(n)=n^4. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^2 >= x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212064 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A212065 Number of (w,x,y,z) with all terms in {1,...,n} and w^2<=x*y*z.

Original entry on oeis.org

0, 1, 12, 57, 185, 459, 974, 1830, 3168, 5158, 7957, 11766, 16830, 23378, 31689, 42041, 54774, 70218, 88757, 110720, 136558, 166715, 201620, 241761, 287646, 339854, 398829, 465198, 539557, 622513, 714762, 816892, 929637, 1053742
Offset: 0

Views

Author

Clark Kimberling, Apr 30 2012

Keywords

Comments

a(n)+A212066(n)=n^4. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^2 <= x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212065 *)
(* Peter J. C. Moses, Apr 13 2012 *)

A212066 Number of (w,x,y,z) with all terms in {1,...,n} and w^2>x*y*z.

Original entry on oeis.org

0, 0, 4, 24, 71, 166, 322, 571, 928, 1403, 2043, 2875, 3906, 5183, 6727, 8584, 10762, 13303, 16219, 19601, 23442, 27766, 32636, 38080, 44130, 50771, 58147, 66243, 75099, 84768, 95238, 106629, 118939, 132179, 146448, 161761, 178106
Offset: 0

Views

Author

Clark Kimberling, Apr 30 2012

Keywords

Comments

a(n)+A212065(n)=n^4. For a guide to related sequences, see A211795.

Crossrefs

Cf. A211795.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^2 > x*y*z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212066 *)
(* Peter J. C. Moses, Apr 13 2012 *)
Previous Showing 31-40 of 202 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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