A120155 a(n) = 10 + floor( (1 + Sum_{j=1..n-1} a(j) )/3 ).

10, 13, 18, 24, 32, 42, 56, 75, 100, 133, 178, 237, 316, 421, 562, 749, 999, 1332, 1776, 2368, 3157, 4209, 5612, 7483, 9977, 13303, 17737, 23650, 31533, 42044, 56059, 74745, 99660, 132880, 177173, 236231, 314975, 419966, 559955, 746607

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) >;
A120155:= func< n | g(n,10,1) >;
[A120155(n): n in [1..60]]; // G. C. Greubel, Jun 20 2023

Mathematica

A120155[n_]:= A120155[n]= 10 +Quotient[1 +Sum[A120155[k], {k,n-1}], 3];
Table[A120155[n], {n,60}] (* G. C. Greubel, Jun 20 2023 *)

SageMath

@CachedFunction
def A120155(n): return 10 +(1+sum(A120155(k) for k in range(1,n)))//3
[A120155(n) for n in range(1,61)] # G. C. Greubel, Jun 20 2023