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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A120158 a(n) = 14 + floor((1 + Sum_{j=1..n-1} a(j))/3).

Original entry on oeis.org

14, 19, 25, 33, 44, 59, 79, 105, 140, 187, 249, 332, 443, 590, 787, 1049, 1399, 1865, 2487, 3316, 4421, 5895, 7860, 10480, 13973, 18631, 24841, 33122, 44162, 58883, 78511, 104681, 139575, 186100, 248133, 330844, 441125, 588167, 784223, 1045630
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/3);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120158:= func< n | g(n, 14, 1) >;
[A120158(n): n in [1..60]]; // G. C. Greubel, Aug 31 2023
  • Mathematica
    nxt[{a_,t_}]:=Module[{c=Floor[(43+t)/3]},{c,t+c}]; Rest[Transpose[ NestList[ nxt,{14,0},40]][[1]]] (* Harvey P. Dale, Jun 12 2014 *)
A120158[n_]:= A120158[n]= 14 +Quotient[1 +Sum[A120158[k], {k,n-1}], 3];
Table[A120158[n], {n, 60}] (* G. C. Greubel, Aug 31 2023 *)
  • SageMath
    @CachedFunction
def A120158(n): return 14 +(1+sum(A120158(k) for k in range(1, n)))//3
[A120158(n) for n in range(1, 61)] # G. C. Greubel, Aug 31 2023

A120159 a(n) = 15 + floor((2 + Sum_{j=1..n-1} a(j))/3).

Original entry on oeis.org

15, 20, 27, 36, 48, 64, 85, 114, 152, 202, 270, 360, 480, 640, 853, 1137, 1516, 2022, 2696, 3594, 4792, 6390, 8520, 11360, 15146, 20195, 26927, 35902, 47870, 63826, 85102, 113469, 151292, 201723, 268964, 358618, 478158, 637544, 850058, 1133411
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/3);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120159:= func< n | g(n, 15, 2) >;
[A120159(n): n in [1..60]]; // G. C. Greubel, Aug 31 2023
  • Mathematica
    A120159[n_]:= A120159[n]= 15 +Quotient[2 +Sum[A120159[k], {k,n-1}], 3];
Table[A120159[n], {n, 60}] (* G. C. Greubel, Aug 31 2023 *)
  • SageMath
    @CachedFunction
def A120159(n): return 15 +(2+sum(A120159(k) for k in range(1, n)))//3
[A120159(n) for n in range(1, 61)] # G. C. Greubel, Aug 31 2023

Extensions

Name edited by G. C. Greubel, Aug 31 2023

A120161 a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/4).

Original entry on oeis.org

2, 2, 3, 4, 5, 6, 7, 9, 11, 14, 18, 22, 28, 35, 43, 54, 68, 85, 106, 132, 165, 207, 258, 323, 404, 505, 631, 789, 986, 1232, 1540, 1925, 2407, 3008, 3760, 4700, 5875, 7344, 9180, 11475, 14344, 17930, 22412, 28015, 35019, 43774, 54717, 68397, 85496, 106870
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/4);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1,a,b)-f(n,a,b) >;
A120161:= func< n | g(n,2,1) >;
[A120161(n): n in [1..60]]; // G. C. Greubel, Sep 02 2023
  • Mathematica
    f[s_]:= Append[s, Floor[(9 +Plus @@ s)/4]]; Nest[f, {2}, 49] (* Robert G. Wilson v, Jul 08 2006 *)
  • SageMath
    @CachedFunction
def f(n,p,q): return p + (q + sum(f(k,p,q) for k in range(1,n)))//4
def A120161(n): return f(n,2,1)
[A120161(n) for n in range(1,61)] # G. C. Greubel, Sep 02 2023

Extensions

More terms from Robert G. Wilson v, Jul 08 2006
Name edited by G. C. Greubel, Sep 02 2023

A120162 a(n) = 3 + floor((2 + Sum_{j=1..n-1} a(j))/4).

Original entry on oeis.org

3, 4, 5, 6, 8, 10, 12, 15, 19, 24, 30, 37, 46, 58, 72, 90, 113, 141, 176, 220, 275, 344, 430, 538, 672, 840, 1050, 1313, 1641, 2051, 2564, 3205, 4006, 5008, 6260, 7825, 9781, 12226, 15283, 19103
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/4);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1,a,b)-f(n,a,b) >;
A120162:= func< n | g(n, 3, 2) >;
[A120162(n): n in [1..60]]; // G. C. Greubel, Sep 02 2023
  • Mathematica
    f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q + Sum[f[k,p,q], {k,n-1}], 4];
A120162[n_]:= f[n,3,2];
Table[A120162[n], {n,60}] (* G. C. Greubel, Sep 02 2023 *)
  • SageMath
    @CachedFunction
def f(n,p,q): return p + (q + sum(f(k,p,q) for k in range(1,n)))//4
def A120162(n): return f(n,3,2)
[A120162(n) for n in range(1,61)] # G. C. Greubel, Sep 02 2023

Extensions

Name edited by G. C. Greubel, Sep 02 2023

A120163 a(n) = 4 + floor((3 + Sum_{j=1..n-1} a(j))/4).

Original entry on oeis.org

4, 5, 7, 8, 10, 13, 16, 20, 25, 31, 39, 49, 61, 76, 95, 119, 149, 186, 233, 291, 364, 455, 568, 710, 888, 1110, 1387, 1734, 2168, 2710, 3387, 4234, 5292, 6615, 8269, 10336, 12920, 16150, 20188, 25235
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/4);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120163:= func< n | g(n, 4, 3) >;
[A120163(n): n in [1..60]]; // G. C. Greubel, Sep 05 2023
  • Mathematica
    l={4};Do[l=AppendTo[l,Floor[(19+Total[l])/4]],{40}];l (* Harvey P. Dale, Sep 23 2011 *)
  • SageMath
    @CachedFunction
def f(n, p, q): return p + (q + sum(f(k, p, q) for k in range(1, n)))//4
def A120163(n): return f(n, 4, 3)
[A120163(n) for n in range(1, 61)] # G. C. Greubel, Sep 05 2023

A120172 a(n) = 3 + floor((2 + Sum_{j=1..n-1} a(j))/5).

Original entry on oeis.org

3, 4, 4, 5, 6, 7, 9, 11, 13, 15, 18, 22, 26, 32, 38, 46, 55, 66, 79, 95, 114, 137, 164, 197, 236, 283, 340, 408, 490, 588, 705, 846, 1015, 1218, 1462, 1754, 2105, 2526, 3031, 3638, 4365, 5238, 6286, 7543, 9052, 10862, 13034, 15641, 18769, 22523, 27028, 32433
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/5);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120172:= func< n | g(n, 3, 2) >;
[A120172(n): n in [1..60]]; // G. C. Greubel, Dec 25 2023
  • Mathematica
    nxt[{a_,ls_}]:=Module[{x=Floor[(17+ls)/5]},{x,ls+x}]; Transpose[ NestList[ nxt,{3,3},60]][[1]] (* Harvey P. Dale, Jun 11 2014 *)
  • SageMath
    @CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//5
def A120172(n): return f(n, 3, 2)
[A120172(n) for n in range(1, 61)] # G. C. Greubel, Dec 25 2023

Extensions

More terms from Harvey P. Dale, Jun 11 2014

A120173 a(n) = 4 + floor((3 + Sum_{j=1..n-1} a(j))/5).

Original entry on oeis.org

4, 5, 6, 7, 9, 10, 12, 15, 18, 21, 26, 31, 37, 44, 53, 64, 77, 92, 110, 132, 159, 191, 229, 275, 330, 396, 475, 570, 684, 821, 985, 1182, 1418, 1702, 2042, 2451, 2941, 3529, 4235, 5082
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088.

Programs

  • Magma
    function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/5);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120173:= func< n | g(n, 4, 3) >;
[A120173(n): n in [1..60]]; // G. C. Greubel, Dec 26 2023
  • Mathematica
    A120173[n_]:= A120173[n]= 4 +Floor[(3 +Sum[a[j], {j,n-1}])/5];
Table[A120173[n], {n, 60}] (* G. C. Greubel, Dec 26 2023 *)
  • SageMath
    @CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//5
def A120173(n): return f(n, 4, 3)
[A120173(n) for n in range(1, 61)] # G. C. Greubel, Dec 26 2023

A120174 a(1)=5; a(n)=floor((29+sum(a(1) to a(n-1)))/5).

Original entry on oeis.org

5, 6, 8, 9, 11, 13, 16, 19, 23, 27, 33, 39, 47, 57, 68, 82, 98, 118, 141, 169, 203, 244, 293, 351, 421, 506, 607, 728, 874, 1049, 1258, 1510, 1812, 2174, 2609, 3131, 3757, 4509, 5410, 6492
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A112088, A072493.

Programs

  • Maple
    R:= 5: s:= 5:
for i from 2 to 100 do
  v:= floor((29+s)/5);
  R:= R,v;
  s:= s+v;
od:
R; # Robert Israel, Sep 11 2024

A120175 a(1)=7; a(n)=floor((35+sum(a(1) to a(n-1)))/5).

Original entry on oeis.org

7, 8, 10, 12, 14, 17, 20, 24, 29, 35, 42, 50, 60, 72, 87, 104, 125, 150, 180, 216, 259, 311, 373, 448, 537, 645, 774, 928, 1114, 1337, 1604, 1925, 2310, 2772, 3326, 3992, 4790, 5748, 6898, 8277
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A112088, A072493.

Programs

  • Mathematica
    nxt[{t_,a_}]:=Module[{k=Floor[(35+t)/5]},{t+k,k}]; NestList[nxt,{7,7},40][[All,2]] (* Harvey P. Dale, Oct 05 2022 *)

A120177 a(1)=9; a(n)=floor((47+sum(a(1) to a(n-1)))/5).

Original entry on oeis.org

9, 11, 13, 16, 19, 23, 27, 33, 39, 47, 56, 68, 81, 97, 117, 140, 168, 202, 242, 291, 349, 419, 502, 603, 723, 868, 1042, 1250, 1500, 1800, 2160, 2592, 3110, 3732, 4479, 5375, 6450, 7740, 9288, 11145
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A112088, A072493.

Programs

  • Mathematica
    nxt[{t_,a_}]:=Module[{c=Floor[(47+t)/5]},{t+c,c}]; NestList[nxt,{9,9},40][[All,2]] (* Harvey P. Dale, Jul 26 2017 *)
Previous Showing 41-50 of 79 results. Next

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