A120151 a(n) = 5 + floor( Sum_{j=1..n-1} a(j)/3 ).

5, 6, 8, 11, 15, 20, 26, 35, 47, 62, 83, 111, 148, 197, 263, 350, 467, 623, 830, 1107, 1476, 1968, 2624, 3499, 4665, 6220, 8293, 11058, 14744, 19658, 26211, 34948, 46597, 62130, 82840, 110453, 147271, 196361, 261815, 349086, 465448, 620598, 827464, 1103285

Offset: 1

Author

Graeme McRae, Jun 10 2006

Keywords

• nonn

Links

• Harvey P. Dale, 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) >;
A120151:= func< n | g(n,5,0) >;
[A120151(n): n in [1..60]]; // G. C. Greubel, Jun 15 2023

Maple

a:= proc(n) option remember;
       5+floor(add(a(j)/3, j=1..n-1))
    end:
seq(a(n), n=1..44);  # Alois P. Heinz, Jun 16 2023

Mathematica

nxt[{t_,n_}]:=Module[{c=Floor[(15+t)/3]},{t+c,c}]; NestList[nxt,{5,5},40][[All,2]] (* Harvey P. Dale, Jun 19 2022 *)

SageMath

@CachedFunction
def A120151(n): return 5 + (sum(A120151(k) for k in range(1, n)))//3
[A120151(n) for n in range(1, 61)] # G. C. Greubel, Jun 15 2023