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

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

Author

Graeme McRae, Jun 10 2006

Keywords

• nonn

Links

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

Crossrefs

Cf. A072493, A073941, A112088.

Cf. A120160 - A120164, A120166 - 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) >;
A120165:= func< n | g(n, 7, 1) >;
[A120165(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023

Maple

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

Mathematica

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

SageMath

@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

Formula

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