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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A110650 n^2 followed by n^4 followed by n followed by n^3.

Original entry on oeis.org

1, 1, 1, 1, 4, 16, 2, 8, 9, 81, 3, 27, 16, 256, 4, 64, 25, 625, 5, 125, 36, 1296, 6, 216, 49, 2401, 7, 343, 64, 4096, 8, 512, 81, 6561, 9, 729, 100, 10000, 10, 1000, 121, 14641, 11, 1331, 144, 20736, 12, 1728, 169, 28561, 13, 2197, 196, 38416, 14, 2744, 225, 50625
Offset: 1

Views

Author

Mohammad K. Azarian, Sep 14 2005

Keywords

Links

Crossrefs

Cf. A000463; A109588; A109594.
Cf. A010873.

Programs

  • GAP
    Flat(List([1..20],n->[n^2,n^4,n,n^3])); # Muniru A Asiru, Apr 08 2018
  • Magma
    &cat[[n^2, n^4, n, n^3]: n in [1..20]]; // Vincenzo Librandi, Nov 25 2012
  • Mathematica
    Flatten[Table[{n^2,n^4,n,n^3},{n,20}]] (* Harvey P. Dale, Oct 10 2012 *)

Formula

a(n) = floor((n+3)/4)^((-8*(n mod 4)^3 + 33*(n mod 4)^2 - 31*(n mod 4) + 18)/6). - Luce ETIENNE, Apr 07 2018
From Chai Wah Wu, Jan 10 2020: (Start)
a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20) for n > 20.
G.f.: x*(x^15 + x^14 - x^13 - x^12 + 3*x^11 - 3*x^10 - 11*x^9 + x^8 - 3*x^7 + 3*x^6 - 11*x^5 + x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)

A109816 n^2 followed by n followed by n^3.

Original entry on oeis.org

1, 1, 1, 4, 2, 8, 9, 3, 27, 16, 4, 64, 25, 5, 125, 36, 6, 216, 49, 7, 343, 64, 8, 512, 81, 9, 729, 100, 10, 1000, 121, 11, 1331, 144, 12, 1728, 169, 13, 2197, 196, 14, 2744, 225, 15, 3375, 256, 16, 4096, 289, 17, 4913, 324, 18, 5832, 361, 19, 6859, 400, 20, 8000
Offset: 1

Views

Author

Mohammad K. Azarian, Aug 30 2005

Keywords

Links

Crossrefs

Cf. A000463.
Cf. A010872.

Programs

  • Magma
    &cat[[n^2,n,n^3]: n in [1..20]]; // Bruno Berselli, Sep 01 2016
  • Mathematica
    Table[{n^2, n, n^3}, {n, 20}] // Flatten (* Bruno Berselli, Sep 01 2016 *)

Formula

From Chai Wah Wu, Jul 16 2016: (Start)
a(n) = 4*a(n-3) - 6*a(n-6) + 4*a(n-9) - a(n-12) for n > 12.
G.f.: x*(x^8 + x^7 - x^6 + 4*x^5 - 2*x^4 + x^2 + x + 1)/((x - 1)^4*(x^2 + x + 1)^4). (End)
a(n) = floor((n+2)/3)^(-(n mod 3)+3). - Luce ETIENNE, Mar 01 2018

A110003 n followed by n^3 followed by n^2 followed by n^4.

Original entry on oeis.org

1, 1, 1, 1, 2, 8, 4, 16, 3, 27, 9, 81, 4, 64, 16, 256, 5, 125, 25, 625, 6, 216, 36, 1296, 7, 343, 49, 2401, 8, 512, 64, 4096, 9, 729, 81, 6561, 10, 1000, 100, 10000, 11, 1331, 121, 14641, 12, 1728, 144, 20736, 13, 2197, 169, 28561, 14, 2744, 196, 38416, 15, 3375
Offset: 1

Views

Author

Mohammad K. Azarian, Sep 02 2005

Keywords

Links

Crossrefs

Cf. A000463, A109588, A109594.

Programs

Formula

a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+4*n^2+32*n+96+(n^3+4*n^2-64)*(-1)^n-(n^3-4*n^2-64)*(-1)^((2*n+5-(-1)^n)/4)+(n^3-4*n^2-32*n+32)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Sep 01 2016
From Chai Wah Wu, Jan 11 2020: (Start)
a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20) for n > 20.
G.f.: x*(-x^15 - x^14 + x^13 + x^12 - 11*x^11 + x^10 + 3*x^9 - 3*x^8 - 11*x^7 + x^6 - 3*x^5 + 3*x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)

A110004 n followed by n^3 followed by n^4 followed by n^2.

Original entry on oeis.org

1, 1, 1, 1, 2, 8, 16, 4, 3, 27, 81, 9, 4, 64, 256, 16, 5, 125, 625, 25, 6, 216, 1296, 36, 7, 343, 2401, 49, 8, 512, 4096, 64, 9, 729, 6561, 81, 10, 1000, 10000, 100, 11, 1331, 14641, 121, 12, 1728, 20736, 144, 13, 2197, 28561, 169, 14, 2744, 38416, 196, 15
Offset: 1

Views

Author

Mohammad K. Azarian, Sep 02 2005

Keywords

Links

Crossrefs

Cf. A000463, A109588, A109594.

Programs

  • Magma
    [&cat[[n,n^3,n^4,n^2]: n in [1..20]]]; // Vincenzo Librandi, Sep 05 2016
  • Mathematica
    Table[n^{1, 3, 4, 2}, {n, 15}] // Flatten (* or *)
Table[(2 n + 3 - (-1)^n + 2 (-1)^((2 n + 5 - (-1)^n)/4)) (n^3 + 7 n^2 + 35 n + 81 - (n^3 - n^2 - 29 n + 49) (-1)^n - (n^3 - n^2 + 3 n - 79) (-1)^((2 n + 5 - (-1)^n)/4) - (n^3 + 7 n^2 + 3 n - 47) (-1)^((2 n + 7 + (-1)^n)/4))/2048, {n, 57}] (* Michael De Vlieger, Sep 03 2016 *)
LinearRecurrence[{0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1},{1,1,1,1,2,8,16,4,3,27,81,9,4,64,256,16,5,125,625,25},60] (* Harvey P. Dale, Jul 19 2024 *)

Formula

a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+7*n^2+35*n+81-(n^3-n^2-29*n+49)*(-1)^n-(n^3-n^2+3*n-79)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+7*n^2+3*n-47)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Sep 03 2016
From Chai Wah Wu, Jan 11 2020: (Start)
a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20) for n > 20.
G.f.: x*(-x^15 - x^14 + x^13 + x^12 + x^11 - 11*x^10 + 3*x^9 - 3*x^8 + x^7 - 11*x^6 - 3*x^5 + 3*x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)

A110008 n followed by n^4 followed by n^3 followed by n^2.

Original entry on oeis.org

1, 1, 1, 1, 2, 16, 8, 4, 3, 81, 27, 9, 4, 256, 64, 16, 5, 625, 125, 25, 6, 1296, 216, 36, 7, 2401, 343, 49, 8, 4096, 512, 64, 9, 6561, 729, 81, 10, 10000, 1000, 100, 11, 14641, 1331, 121, 12, 20736, 1728, 144, 13, 28561, 2197, 169, 14, 38416, 2744, 196, 15
Offset: 1

Views

Author

Mohammad K. Azarian, Sep 02 2005

Keywords

Links

Crossrefs

Cf. A000463, A109588, A109594.

Programs

  • Mathematica
    Flatten[Table[{n,n^Range[4,2,-1]},{n,15}]] (* Harvey P. Dale, Aug 11 2011 *)
  • PARI
    s=[]; for(n=1, 100, s=concat(s, [n,n^4,n^3,n^2])); s \\ Colin Barker, Dec 13 2014

Formula

G.f.: -x*(x^15-x^14+x^13-x^12-x^11-3*x^10+11*x^9+3*x^8-x^7+3*x^6+11*x^5-3*x^4+x^3+x^2+x+1) / ((x-1)^5*(x+1)^5*(x^2+1)^5). - Colin Barker, Dec 13 2014
a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+10*n^2+36*n+76+(n^3+2*n^2+20*n-60)*(-1)^n+(n^3+2*n^2-12*n+68)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+10*n^2+4*n-52)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Aug 27 2016

A110485 n^2 followed by n followed by n^4 followed by n^3.

Original entry on oeis.org

1, 1, 1, 1, 4, 2, 16, 8, 9, 3, 81, 27, 16, 4, 256, 64, 25, 5, 625, 125, 36, 6, 1296, 216, 49, 7, 2401, 343, 64, 8, 4096, 512, 81, 9, 6561, 729, 100, 10, 10000, 1000, 121, 11, 14641, 1331, 144, 12, 20736, 1728, 169, 13, 28561, 2197, 196, 14, 38416, 2744, 225, 15
Offset: 1

Views

Author

Mohammad K. Azarian, Sep 14 2005

Keywords

Crossrefs

Cf. A000463, A109588, A109594.

Programs

  • Mathematica
    Flatten[Table[{n^2,n,n^4,n^3},{n,20}]] (* Harvey P. Dale, Oct 24 2013 *)

Formula

a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+7*n^2+19*n+113-(n^3-n^2+19*n-15)*(-1)^n-(n^3+7*n^2-13*n-111)*(-1)^((2*n+5-(-1)^n)/4)-(n^3-n^2-13*n+17)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Sep 01 2016
From Chai Wah Wu, Jan 11 2020: (Start)
a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20) for n > 20.
G.f.: x*(x^15 - x^14 + x^13 - x^12 + 3*x^11 - 11*x^10 - 3*x^9 + x^8 - 3*x^7 - 11*x^6 + 3*x^5 + x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)

A110651 n^2 followed by n^4 followed by n^3 followed by n.

Original entry on oeis.org

1, 1, 1, 1, 4, 16, 8, 2, 9, 81, 27, 3, 16, 256, 64, 4, 25, 625, 125, 5, 36, 1296, 216, 6, 49, 2401, 343, 7, 64, 4096, 512, 8, 81, 6561, 729, 9, 100, 10000, 1000, 10, 121, 14641, 1331, 11, 144, 20736, 1728, 12, 169, 28561, 2197, 13, 196, 38416, 2744, 14, 225
Offset: 1

Views

Author

Mohammad K. Azarian, Sep 14 2005

Keywords

Links

Crossrefs

Cf. A000463, A109588, A109594.

Programs

  • Magma
    &cat[[n^2, n^4, n^3, n]: n in [1..20]]; // Vincenzo Librandi, Feb 06 2013
  • Mathematica
    Flatten[Table[{n^2, n^4, n^3, n}, {n, 40}]](* Vincenzo Librandi, Feb 06 2013 *)
LinearRecurrence[{0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1},{1,1,1,1,4,16,8,2,9,81,27,3,16,256,64,4,25,625,125,5},60] (* Harvey P. Dale, Sep 20 2023 *)
  • PARI
    Vec(x*(1+x+x^2+x^3-x^4+11*x^5+3*x^6-3*x^7-x^8+11*x^9-3*x^10+3*x^11+x^12+x^13-x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5) + O(x^30)) \\ Colin Barker, Sep 02 2016

Formula

a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+10*n^2+36*n+124+(n^3+2*n^2-12*n+20)*(-1)^n+(n^3+2*n^2+20*n-12)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+10*n^2+4*n-100)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Sep 02 2016
G.f.: x*(1+x+x^2+x^3-x^4+11*x^5+3*x^6-3*x^7-x^8+11*x^9-3*x^10+3*x^11 +x^12+x^13-x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5). - Colin Barker, Sep 02 2016
a(n) = 5*a(n-4)-10*a(n-8)+10*a(n-12)-5*a(n-16)+a(n-20). - Wesley Ivan Hurt, Jun 09 2023

A110652 n^2 followed by n^3 followed by n^4 followed by n.

Original entry on oeis.org

1, 1, 1, 1, 4, 8, 16, 2, 9, 27, 81, 3, 16, 64, 256, 4, 25, 125, 625, 5, 36, 216, 1296, 6, 49, 343, 2401, 7, 64, 512, 4096, 8, 81, 729, 6561, 9, 100, 1000, 10000, 10, 121, 1331, 14641, 11, 144, 1728, 20736, 12, 169, 2197, 28561, 13, 196, 2744, 38416, 14, 225
Offset: 1

Views

Author

Mohammad K. Azarian, Sep 14 2005

Keywords

Links

Crossrefs

Cf. A000463, A109588, A109594.

Programs

  • Magma
    &cat[[n^2, n^3, n^4, n]: n in [1..20]]; // Vincenzo Librandi, Feb 06 2013
  • Mathematica
    Flatten[Table[{n^2, n^3, n^4, n}, {n, 40}]] (* Vincenzo Librandi, Feb 06 2013 *)
  • PARI
    Vec(x*(1+x+x^2+x^3-x^4+3*x^5+11*x^6-3*x^7-x^8-3*x^9+11*x^10+3*x^11+x^12-x^13+x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5) + O(x^20)) \\ Colin Barker, Aug 18 2016

Formula

a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+7*n^2+35*n+129-(n^3-n^2+3*n-31)*(-1)^n-(n^3-n^2-29*n+1)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+7*n^2+3*n-95)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Aug 17 2016
G.f.: x*(1+x+x^2+x^3-x^4+3*x^5+11*x^6-3*x^7-x^8-3*x^9+11*x^10+3*x^11+x^12-x^13+x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5). - Colin Barker, Aug 18 2016

A110653 n^2 followed by n^3 followed by n followed by n^4.

Original entry on oeis.org

1, 1, 1, 1, 4, 8, 2, 16, 9, 27, 3, 81, 16, 64, 4, 256, 25, 125, 5, 625, 36, 216, 6, 1296, 49, 343, 7, 2401, 64, 512, 8, 4096, 81, 729, 9, 6561, 100, 1000, 10, 10000, 121, 1331, 11, 14641, 144, 1728, 12, 20736, 169, 2197, 13, 28561, 196, 2744, 14, 38416, 225, 3375
Offset: 1

Views

Author

Mohammad K. Azarian, Sep 14 2005

Keywords

Links

Crossrefs

Cf. A000463; A109588; A109594.
Cf. A010873.

Programs

  • Magma
    &cat[[n^2, n^3, n, n^4]: n in [1..20]]; // Vincenzo Librandi, Feb 06 2013
  • Mathematica
    Flatten[Table[{n^2, n^3, n, n^4}, {n, 40}]] (* Vincenzo Librandi, Feb 06 2013 *)

Formula

a(n) = floor((n+3)/4)^((-2*(n mod 4)^3+9*(n mod 4)^2 - 11*(n mod 4) + 8)/2). - Luce ETIENNE, Apr 07 2018
From Chai Wah Wu, Jan 11 2020: (Start)
a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20) for n > 20.
G.f.: x*(-x^15 + x^14 + x^13 - x^12 - 11*x^11 - 3*x^10 + 3*x^9 + x^8 - 11*x^7 + 3*x^6 - 3*x^5 + x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)

A109595 n^3 followed by n^2 followed by n.

Original entry on oeis.org

1, 1, 1, 8, 4, 2, 27, 9, 3, 64, 16, 4, 125, 25, 5, 216, 36, 6, 343, 49, 7, 512, 64, 8, 729, 81, 9, 1000, 100, 10, 1331, 121, 11, 1728, 144, 12, 2197, 169, 13, 2744, 196, 14, 3375, 225, 15, 4096, 256, 16, 4913, 289, 17, 5832, 324, 18, 6859, 361, 19, 8000, 400, 20
Offset: 1

Views

Author

Mohammad K. Azarian, Aug 30 2005

Keywords

Links

Crossrefs

Cf. A000463.
Cf. A010872.

Programs

  • Mathematica
    Flatten[Table[{n^3,n^2,n},{n,20}]] (* or *) LinearRecurrence[{0,0,4,0,0,-6,0,0,4,0,0,-1},{1,1,1,8,4,2,27,9,3,64,16,4},60] (* Harvey P. Dale, Aug 22 2014 *)

Formula

a(n) = floor((n+2)/3)^((-3*(n mod 3)^2+7*(n mod 3)+2)/2). - Luce ETIENNE, Mar 01 2018
Previous Showing 11-20 of 24 results. Next

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