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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A120142 a(n) = 16 + floor(Sum_{j=1..n-1} a(j)/2).

Original entry on oeis.org

16, 24, 36, 54, 81, 121, 182, 273, 409, 614, 921, 1381, 2072, 3108, 4662, 6993, 10489, 15734, 23601, 35401, 53102, 79653, 119479, 179219, 268828, 403242, 604863, 907295, 1360942, 2041413, 3062120, 4593180, 6889770, 10334655, 15501982
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120141, A120143 - A120209.

Programs

  • Mathematica
    Nest[Append[#,16+Floor[Total[#]/2]]&,{16},40]  (* Harvey P. Dale, Apr 20 2011 *)
  • SageMath
    @CachedFunction
def A120142(n): return 16 + (sum(A120142(k) for k in range(1,n)))//2
[A120142(n) for n in range(1,60)] # G. C. Greubel, May 11 2023

A120143 a(n) = 17 + floor( (1 + Sum_{j=0..n-1} a(j))/2 ).

Original entry on oeis.org

17, 26, 39, 58, 87, 131, 196, 294, 441, 662, 993, 1489, 2234, 3351, 5026, 7539, 11309, 16963, 25445, 38167, 57251, 85876, 128814, 193221, 289832, 434748, 652122, 978183, 1467274, 2200911, 3301367, 4952050, 7428075, 11142113, 16713169
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120142, A120144 - A120209.

Programs

  • Mathematica
    nxt[{t_,a_}]:=Module[{c=17+Floor[(1+t)/2]},{t+c,c}]; NestList[nxt,{17,17},60][[All,2]] (* Harvey P. Dale, Dec 25 2020 *)
  • SageMath
    @CachedFunction
def A120143(n): return 17 + (1 +sum(A120143(k) for k in range(1,n)))//2
[A120143(n) for n in range(1,60)] # G. C. Greubel, May 11 2023

A120144 a(n) = 19 + floor( Sum_{j=1..n-1} a(j) / 2 ).

Original entry on oeis.org

19, 28, 42, 63, 95, 142, 213, 320, 480, 720, 1080, 1620, 2430, 3645, 5467, 8201, 12301, 18452, 27678, 41517, 62275, 93413, 140119, 210179, 315268, 472902, 709353, 1064030, 1596045, 2394067, 3591101, 5386651, 8079977, 12119965, 18179948
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120143, A120145 - A120209.

Programs

  • Mathematica
    a[n_]:= a[n]= 19 +Quotient[Sum[a[k], {k,n-1}], 2];
Table[a[n], {n,60}] (* G. C. Greubel, May 14 2023 *)
  • SageMath
    @CachedFunction
def A120144(n): return 19 + sum(A120144(k) for k in range(1,n))//2
[A120144(n) for n in range(1,61)] # G. C. Greubel, May 14 2023

A120166 a(n) = 8 + floor((2 + Sum_{j=1..n-1} a(j))/4).

Original entry on oeis.org

8, 10, 13, 16, 20, 25, 31, 39, 49, 61, 76, 95, 119, 149, 186, 232, 290, 363, 454, 567, 709, 886, 1108, 1385, 1731, 2164, 2705, 3381, 4226, 5283, 6603, 8254, 10318, 12897, 16121, 20152, 25190, 31487, 39359, 49199
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.
Cf. A120160 - A120165, A120167 - A120169.

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) >;
A120166:= func< n | g(n, 8, 2) >;
[A120166(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023
  • Mathematica
    f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];
A120166[n_]:= f[n,8,2];
Table[A120166[n], {n, 60}] (* G. C. Greubel, Sep 09 2023 *)
  • SageMath
    @CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
def A120166(n): return f(n, 8, 2)
[A120166(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023

A120167 a(n) = 9 + floor((3 + Sum_{j=1..n-1} a(j))/4).

Original entry on oeis.org

9, 12, 15, 18, 23, 29, 36, 45, 56, 70, 88, 110, 137, 171, 214, 268, 335, 418, 523, 654, 817, 1021, 1277, 1596, 1995, 2494, 3117, 3896, 4870, 6088, 7610, 9512, 11890, 14863, 18579, 23223, 29029, 36286, 45358, 56697
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.
Cf. A120160 - A120166, A120168, A120169.

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) >;
A120167:= func< n | g(n, 9, 3) >;
[A120167(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023
  • Mathematica
    nxt[{t_,a_}]:=Module[{c=Floor[(39+t)/4]},{t+c,c}]; NestList[nxt,{9,9},40][[All,2]] (* Harvey P. Dale, Apr 24 2019 *)
  • SageMath
    @CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
def A120167(n): return f(n, 9, 3)
[A120167(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023

A120168 a(n) = 11 + floor(Sum_{j-1..n-1} a(j)/4).

Original entry on oeis.org

11, 13, 17, 21, 26, 33, 41, 51, 64, 80, 100, 125, 156, 195, 244, 305, 381, 476, 595, 744, 930, 1163, 1453, 1817, 2271, 2839, 3548, 4435, 5544, 6930, 8663, 10828, 13535, 16919, 21149, 26436, 33045, 41306, 51633, 64541
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.
Cf. A120160 - A120167, A120169.

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) >;
A120168:= func< n | g(n, 11, 0) >;
[A120168(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023
  • Mathematica
    f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];
A120168[n_]:= f[n, 11, 0];
Table[A120168[n], {n, 60}] (* G. C. Greubel, Sep 09 2023 *)
  • SageMath
    @CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
def A120168(n): return f(n, 11, 0)
[A120168(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023

A120145 a(n) = 20 + floor( (1 + Sum_{j=1..n-1} a(j)) / 2 ).

Original entry on oeis.org

20, 30, 45, 68, 102, 153, 229, 344, 516, 774, 1161, 1741, 2612, 3918, 5877, 8815, 13223, 19834, 29751, 44627, 66940, 100410, 150615, 225923, 338884, 508326, 762489, 1143734, 1715601, 2573401, 3860102, 5790153, 8685229, 13027844
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120144, A120146 - A120209.

Programs

  • Mathematica
    a[n_]:= a[n]= 20 +Quotient[1 +Sum[a[k], {k,n-1}], 2];
Table[a[n], {n,60}] (* G. C. Greubel, May 14 2023 *)
  • SageMath
    @CachedFunction
def A120145(n): return 20 + (1+sum(A120145(k) for k in range(1,n)))//2
[A120145(n) for n in range(1,61)] # G. C. Greubel, May 14 2023

A120146 a(n) = 22 + floor( Sum_{j=1..n-1} a(j)/2 ).

Original entry on oeis.org

22, 33, 49, 74, 111, 166, 249, 374, 561, 841, 1262, 1893, 2839, 4259, 6388, 9582, 14373, 21560, 32340, 48510, 72765, 109147, 163721, 245581, 368372, 552558, 828837, 1243255, 1864883, 2797324, 4195986, 6293979, 9440969, 14161453
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A112088, A072493.

Programs

A120149 a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/3).

Original entry on oeis.org

2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 38, 50, 67, 89, 119, 159, 212, 282, 376, 502, 669, 892, 1189, 1586, 2114, 2819, 3759, 5012, 6682, 8910, 11880, 15840, 21120, 28160, 37546, 50062, 66749, 88999, 118665, 158220, 210960, 281280, 375040, 500053, 666738
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A072493, A073941, A112088.

Programs

  • Mathematica
    f[s_] := Append[s, Floor[(7 + Plus @@ s)/3]]; Nest[f, {2}, 44] (*  Robert G. Wilson v, Jul 08 2006 *)
  • SageMath
    @CachedFunction
def A120149(n): return 2 + (1+sum(A120149(k) for k in range(1,n)))//3
[A120149(n) for n in range(1, 61)] # G. C. Greubel, Jun 04 2023

Extensions

More terms from Robert G. Wilson v, Jul 08 2006

A120164 a(n) = 6 + floor( Sum_{j=1..n-1} a(j)/4 ).

Original entry on oeis.org

6, 7, 9, 11, 14, 17, 22, 27, 34, 42, 53, 66, 83, 103, 129, 161, 202, 252, 315, 394, 492, 615, 769, 961, 1202, 1502, 1878, 2347, 2934, 3667, 4584, 5730, 7163, 8953, 11192, 13990, 17487, 21859, 27324, 34155
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) >;
A120164:= func< n | g(n, 6, 0) >;
[A120164(n): n in [1..60]]; // G. C. Greubel, Sep 05 2023
  • Mathematica
    f[n_, p_, q_]:= f[n, p, q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];
A120164[n_]:= f[n,6,0];
Table[A120164[n], {n, 60}] (* G. C. Greubel, Sep 05 2023 *)
  • SageMath
    @CachedFunction
def f(n,p,q): return p + (q +sum(f(k,p,q) for k in range(1, n)))//4
def A120164(n): return f(n, 6, 0)
[A120164(n) for n in range(1, 61)] # G. C. Greubel, Sep 05 2023
Previous Showing 21-30 of 82 results. Next

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