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.

Showing 1-10 of 12 results. Next

A120134 a(n) = 4 + floor(Sum_{k=1..n-1} a(k) / 2).

Original entry on oeis.org

4, 6, 9, 13, 20, 30, 45, 67, 101, 151, 227, 340, 510, 765, 1148, 1722, 2583, 3874, 5811, 8717, 13075, 19613, 29419, 44129, 66193, 99290, 148935, 223402, 335103, 502655, 753982, 1130973, 1696460, 2544690, 3817035, 5725552, 8588328, 12882492
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120135 - A120209, A172161.

Programs

  • Maple
    a := proc(n) option remember; 4 + iquo(add(a(k), k = 1..n-1), 2) end:
seq(a(n), n = 1..37); # Peter Luschny, May 07 2023
  • Mathematica
    f[s_]:= Append[s, 4+Floor[Plus @@ s/2]]; Nest[f, {4}, 37] (* Robert G. Wilson v, Jun 10 2006 *)
  • SageMath
    @CachedFunction
def A120134(n): return 4 + sum(A120134(k) for k in range(1,n))//2
print([A120134(n) for n in range(1,41)])  # G. C. Greubel, May 07 2023

Formula

a(n) ~ c * (3/2)^n, where c = 3.9320886310283094862025842648411406926537121258867950257873967568454133192... - Vaclav Kotesovec, May 07 2023

Extensions

Name edited by Peter Luschny, May 07 2023

A120135 a(n) = 5 + floor((1 + Sum_{j=1..n-1} a(j)) / 2).

Original entry on oeis.org

5, 8, 12, 18, 27, 40, 60, 90, 135, 203, 304, 456, 684, 1026, 1539, 2309, 3463, 5195, 7792, 11688, 17532, 26298, 39447, 59171, 88756, 133134, 199701, 299552, 449328, 673992, 1010988, 1516482, 2274723, 3412084, 5118126, 7677189, 11515784
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134, A120136 - A120209.

Programs

  • Mathematica
    a[n_]:= a[n]= 5 +Floor[(1+Sum[a[k], {k,n-1}])/2];
Table[a[n], {n,60}] (* G. C. Greubel, May 07 2023 *)
  • SageMath
    @CachedFunction
def A120135(n): return 5 + (1 + sum(A120135(k) for k in range(1,n)))//2
[A120135(n) for n in range(1,61)] # G. C. Greubel, May 07 2023

Formula

a(n) ~ c * (3/2)^n, where c = 3.514931952760438754899508881646642282344325354834703833076259269449577... - Vaclav Kotesovec, May 07 2023

A120136 a(n) = 7 + floor(Sum_{j=1..n-1} a(j) / 2).

Original entry on oeis.org

7, 10, 15, 23, 34, 51, 77, 115, 173, 259, 389, 583, 875, 1312, 1968, 2952, 4428, 6642, 9963, 14945, 22417, 33626, 50439, 75658, 113487, 170231, 255346, 383019, 574529, 861793, 1292690, 1939035, 2908552, 4362828, 6544242, 9816363, 14724545
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134, A120135, A120137 - A120209.

Programs

  • Mathematica
    nxt[{t_,a_}] := Module[{c=7+Floor[t/2]},{t+c,c}];
NestList[nxt,{7,7},40][[All,2]] (* Harvey P. Dale, Jan 13 2017 *)
  • SageMath
    @CachedFunction
def A120136(n): return 7 +sum(A120136(k) for k in range(1,n))//2
[A120136(n) for n in range(1,60)] # G. C. Greubel, May 08 2023

A120137 a(n) = 8 + floor( (1 + Sum_{j=1..n-1} a(j)) / 2).

Original entry on oeis.org

8, 12, 18, 27, 41, 61, 92, 138, 207, 310, 465, 698, 1047, 1570, 2355, 3533, 5299, 7949, 11923, 17885, 26827, 40241, 60361, 90542, 135813, 203719, 305579, 458368, 687552, 1031328, 1546992, 2320488, 3480732, 5221098, 7831647, 11747471, 17621206
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120136, A120138 - A120209.

Programs

  • Mathematica
    a[n_]:= a[n]= 8 +Floor[(1 +Sum[a[k], {k,n-1}])/2];
Table[a[n], {n,60}] (* G. C. Greubel, May 08 2023 *)
nxt[{t_,a_}]:=Module[{c=8+Floor[(1+t)/2]},{t+c,c}]; NestList[nxt,{8,8},40][[;;,2]] (* Harvey P. Dale, Sep 10 2023 *)
  • SageMath
    @CachedFunction
def A120137(n): return 8 +(1 +sum(A120137(k) for k in range(1,n)))//2
[A120137(n) for n in range(1,60)] # G. C. Greubel, May 08 2023

A120138 a(n) = 10 + floor(Sum_{j=1..n-1} a(j) / 2).

Original entry on oeis.org

10, 15, 22, 33, 50, 75, 112, 168, 252, 378, 567, 851, 1276, 1914, 2871, 4307, 6460, 9690, 14535, 21803, 32704, 49056, 73584, 110376, 165564, 248346, 372519, 558779, 838168, 1257252, 1885878, 2828817, 4243226, 6364839, 9547258, 14320887
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120137, A120139 - A120209.

Programs

  • Mathematica
    a[n_]:= a[n]= 10 +Quotient[Sum[a[k], {k,n-1}],2];
Table[a[n], {n,60}] (* G. C. Greubel, May 08 2023 *)
  • SageMath
    @CachedFunction
def A120138(n): return 10 +sum(A120138(k) for k in range(1,n))//2
[A120138(n) for n in range(1,60)] # G. C. Greubel, May 08 2023

A120139 a(n) = 11 + floor( (1 + Sum_{j=1..n-1} a(j)) / 2).

Original entry on oeis.org

11, 17, 25, 38, 57, 85, 128, 192, 288, 432, 648, 972, 1458, 2187, 3280, 4920, 7380, 11070, 16605, 24908, 37362, 56043, 84064, 126096, 189144, 283716, 425574, 638361, 957542, 1436313, 2154469, 3231704, 4847556, 7271334, 10907001, 16360501
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120138, A120140 - A120209.

Programs

  • Mathematica
    a[n_]:= a[n]= 11 +Quotient[1 + Sum[a[k], {k,n-1}], 2];
Table[a[n], {n,60}] (* G. C. Greubel, May 08 2023 *)
  • SageMath
    @CachedFunction
def A120139(n): return 11 +(1 +sum(A120139(k) for k in range(1,n)))//2
[A120139(n) for n in range(1,60)]  # G. C. Greubel, May 08 2023

A120140 a(n) = 13 + floor(Sum_{j=1..n-1} a(j)/2).

Original entry on oeis.org

13, 19, 29, 43, 65, 97, 146, 219, 328, 492, 738, 1107, 1661, 2491, 3737, 5605, 8408, 12612, 18918, 28377, 42565, 63848, 95772, 143658, 215487, 323230, 484845, 727268, 1090902, 1636353, 2454529, 3681794, 5522691, 8284036, 12426054, 18639081
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120139, A120141 - A120209.

Programs

  • Mathematica
    a[n_]:= a[n]= 13 +Quotient[Sum[a[k], {k,n-1}], 2];
Table[a[n], {n,60}] (* G. C. Greubel, May 11 2023 *)
  • SageMath
    @CachedFunction
def A120140(n): return 13 + sum(A120140(k) for k in range(1,n))//2
[A120140(n) for n in range(1,60)] # G. C. Greubel, May 11 2023

A120141 a(n) = 14 + floor( (1 + Sum_{j=0..n-1} a(j)) / 2).

Original entry on oeis.org

14, 21, 32, 48, 72, 108, 162, 243, 364, 546, 819, 1229, 1843, 2765, 4147, 6221, 9331, 13997, 20995, 31493, 47239, 70859, 106288, 159432, 239148, 358722, 538083, 807125, 1210687, 1816031, 2724046, 4086069, 6129104, 9193656, 13790484
Offset: 1

Views

Author

Graeme McRae, Jun 10 2006

Keywords

Links

Crossrefs

Cf. A073941, A072493, A112088, A120134 - A120140, A120142 - A120209.

Programs

  • Mathematica
    nxt[{t_,a_}]:=Module[{a2=14+Floor[(1+t)/2]},{t+a2,a2}]; NestList[nxt,{0,14},60][[All,2]]//Rest (* Harvey P. Dale, Nov 28 2018 *)
  • SageMath
    @CachedFunction
def A120141(n): return 14 +(1 +sum(A120141(k) for k in range(1,n)))//2
[A120141(n) for n in range(1,60)] # G. C. Greubel, May 11 2023

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
Showing 1-10 of 12 results. Next

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