A120152 a(n) = 6 + floor((1 + Sum_{j=1..n-1} a(j))/3).

6, 8, 11, 14, 19, 25, 34, 45, 60, 80, 107, 142, 190, 253, 337, 450, 600, 800, 1066, 1422, 1896, 2528, 3370, 4494, 5992, 7989, 10652, 14203, 18937, 25249, 33666, 44888, 59850, 79800, 106400, 141867, 189156, 252208, 336277, 448370

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)/3);
    end for;
  return t;
end function;
g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
A120152:= func< n | g(n,6,1) >;
[A120152(n): n in [1..60]]; // G. C. Greubel, Jun 15 2023

Mathematica

Module[{lista={6}},Do[AppendTo[lista,Floor[(19+Total[lista])/3]],{40}];lista] (* Harvey P. Dale, Jun 11 2013 *)
nxt[{s_,a_}]:=Module[{x=Floor[(19+s)/3]},{s+x,x}]; NestList[nxt,{6,6},40][[;;,2]] (* Harvey P. Dale, Mar 26 2023 *)

SageMath

@CachedFunction
def A120152(n): return 6 + (1 + sum(A120152(k) for k in range(1,n)))//3
[A120152(n) for n in range(1, 61)] # G. C. Greubel, Jun 15 2023