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.

Previous Showing 11-15 of 15 results.

A212518 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y>3z.

Original entry on oeis.org

0, 0, 0, 0, 2, 8, 18, 45, 84, 144, 240, 375, 540, 792, 1092, 1470, 1960, 2560, 3240, 4131, 5130, 6300, 7700, 9317, 11088, 13248, 15600, 18252, 21294, 24696, 28350, 32625, 37200, 42240, 47872, 54043, 60588, 68040, 75924, 84474, 93860, 104000, 114660, 126567
Offset: 0

Views

Author

Clark Kimberling, May 20 2012

Keywords

Comments

For a guide to related sequences, see A211795.

Links

Crossrefs

Cf. A211795, A212508.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w > 2 x && y > 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212518 *)
  • PARI
    concat(vector(4), Vec(x^4*(2 +8*x +14*x^2 +25*x^3 +34*x^4 +34*x^5 +32*x^6 +32*x^7 +20*x^8 +10*x^9 +4*x^10 +x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+ a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
G.f.: x^4*(2 +8*x +14*x^2 +25*x^3 +34*x^4 +34*x^5 +32*x^6 +32*x^7 +20*x^8 +10*x^9 +4*x^10 +x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 11 2015

A212519 Number of (w,x,y,z) with all terms in {1,...,n} and w>2x and y>=3z.

Original entry on oeis.org

0, 0, 0, 1, 4, 12, 30, 63, 108, 192, 300, 450, 660, 936, 1260, 1715, 2240, 2880, 3672, 4617, 5670, 7000, 8470, 10164, 12144, 14400, 16848, 19773, 22932, 26460, 30450, 34875, 39600, 45056, 50864, 57222, 64260, 71928, 80028, 89167, 98800, 109200, 120540
Offset: 0

Views

Author

Clark Kimberling, May 20 2012

Keywords

Comments

For a guide to related sequences, see A211795.

Links

Crossrefs

Cf. A211795, A212508.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w > 2 x && y >= 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212519 *)
  • PARI
    concat(vector(3), Vec(x^3*(1 +4*x +10*x^2 +20*x^3 +32*x^4 +32*x^5 +34*x^6 +34*x^7 +25*x^8 +14*x^9 +8*x^10 +2*x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+ a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
G.f.: x^3*(1 +4*x +10*x^2 +20*x^3 +32*x^4 +32*x^5 +34*x^6 +34*x^7 +25*x^8 +14*x^9 +8*x^10 +2*x^11) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 11 2015

A212520 Number of (w,x,y,z) with all terms in {1,...,n} and w>=2x and y<3z.

Original entry on oeis.org

0, 0, 4, 16, 56, 132, 279, 504, 880, 1380, 2125, 3090, 4392, 6006, 8134, 10640, 13824, 17568, 22113, 27360, 33700, 40810, 49247, 58740, 69696, 81900, 95992, 111384, 128968, 148260, 169875, 193440, 219904, 248336, 280041, 314262, 351864, 392274, 436810
Offset: 0

Views

Author

Clark Kimberling, May 20 2012

Keywords

Comments

For a guide to related sequences, see A211795.

Links

Crossrefs

Cf. A211795, A212508.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w >= 2 x && y < 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212520 *)
  • PARI
    concat([0,0], Vec(x^2*(4 +16*x +48*x^2 +92*x^3 +139*x^4 +160*x^5 +178*x^6 +162*x^7 +132*x^8 +86*x^9 +46*x^10 +14*x^11 +3*x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+ a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
G.f.: x^2*(4 +16*x +48*x^2 +92*x^3 +139*x^4 +160*x^5 +178*x^6 +162*x^7 +132*x^8 +86*x^9 +46*x^10 +14*x^11 +3*x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 11 2015

A212521 Number of (w,x,y,z) with all terms in {1,...,n} and w>=2x and y<=3z.

Original entry on oeis.org

0, 0, 4, 18, 60, 138, 297, 528, 912, 1440, 2200, 3180, 4536, 6174, 8330, 10920, 14144, 17928, 22599, 27900, 34300, 41580, 50094, 59664, 70848, 83148, 97344, 113022, 130732, 150150, 172125, 195840, 222464, 251328, 283220, 317628, 355752, 396378, 441142
Offset: 0

Views

Author

Clark Kimberling, May 20 2012

Keywords

Comments

For a guide to related sequences, see A211795.

Links

Crossrefs

Cf. A211795, A212508.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w >= 2 x && y <= 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212521 *)
  • PARI
    concat([0,0], Vec(x^2*(4 +18*x +52*x^2 +94*x^3 +145*x^4 +166*x^5 +174*x^6 +160*x^7 +133*x^8 +80*x^9 +40*x^10 +12*x^11 +2*x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+ a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
G.f.: x^2*(4 +18*x +52*x^2 +94*x^3 +145*x^4 +166*x^5 +174*x^6 +160*x^7 +133*x^8 +80*x^9 +40*x^10 +12*x^11 +2*x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 11 2015

A212522 Number of (w,x,y,z) with all terms in {1,...,n} and w>=2x and y>3z.

Original entry on oeis.org

0, 0, 0, 0, 4, 12, 27, 60, 112, 180, 300, 450, 648, 924, 1274, 1680, 2240, 2880, 3645, 4590, 5700, 6930, 8470, 10164, 12096, 14352, 16900, 19656, 22932, 26460, 30375, 34800, 39680, 44880, 50864, 57222, 64152, 71820, 80142, 88920, 98800, 109200, 120393
Offset: 0

Views

Author

Clark Kimberling, May 20 2012

Keywords

Comments

For a guide to related sequences, see A211795.

Links

Crossrefs

Cf. A211795, A212508.

Programs

  • Mathematica
    t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w >= 2 x && y > 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212522 *)
  • PARI
    concat(vector(4), Vec(x^4*(4 +12*x +19*x^2 +28*x^3 +38*x^4 +34*x^5 +31*x^6 +26*x^7 +16*x^8 +6*x^9 +2*x^10) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+ a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
G.f.: x^4*(4 +12*x +19*x^2 +28*x^3 +38*x^4 +34*x^5 +31*x^6 +26*x^7 +16*x^8 +6*x^9 +2*x^10) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 11 2015
Previous Showing 11-15 of 15 results.

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