A120169 -id:A120169 - cp's OEIS frontend

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

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

Graeme McRae, Jun 10 2006

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A072493, A073941, A112088.

Cf. A120160 - A120165, A120167 - A120169.

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

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 *)

@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

Graeme McRae, Jun 10 2006

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A072493, A073941, A112088.

Cf. A120160 - A120166, A120168, A120169.

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

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 *)

@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

Graeme McRae, Jun 10 2006

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A072493, A073941, A112088.

Cf. A120160 - A120167, A120169.

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

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 *)

@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

A120165 a(n) = 7 + floor((1 + Sum_{j=1..n-1} a(j))/4).

Original entry on oeis.org

7, 9, 11, 14, 17, 21, 27, 33, 42, 52, 65, 81, 102, 127, 159, 199, 248, 310, 388, 485, 606, 758, 947, 1184, 1480, 1850, 2312, 2890, 3613, 4516, 5645, 7056, 8820, 11025, 13782, 17227, 21534, 26917, 33647, 42058

Offset: 1

Graeme McRae, Jun 10 2006

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A072493, A073941, A112088.

Cf. A120160 - A120164, A120166 - A120169.

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) >;
A120165:= func< n | g(n, 7, 1) >;
[A120165(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023

A[1]:= 7: S:= 7:
for n from 2 to 100 do A[n]:= floor((29 + S)/4); S:= S + A[n] od:
seq(A[i],i=1..100); # Robert Israel, Mar 20 2017

a = {7}; Do[AppendTo[a, Floor[(29 + Total@ a)/4]], {i, 2, 40}]; a (* Michael De Vlieger, Mar 20 2017 *)

@CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
def A120165(n): return f(n, 7, 1)
[A120165(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023

a(n) ~ c (5/4)^n with c approximately 5.5905081519. - Robert Israel, Mar 20 2017

cp's OEIS Frontend

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

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

A120165 a(n) = 7 + floor((1 + Sum_{j=1..n-1} a(j))/4).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

SageMath

Formula