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

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

Author

Graeme McRae, Jun 10 2006

Keywords

• nonn

Links

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

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