A120154 a(n) = 9 + floor( Sum_{j=1..n-1} a(j)/3 ).

9, 12, 16, 21, 28, 37, 50, 66, 88, 118, 157, 209, 279, 372, 496, 661, 882, 1176, 1568, 2090, 2787, 3716, 4955, 6606, 8808, 11744, 15659, 20879, 27838, 37118, 49490, 65987, 87983, 117310, 156414, 208552, 278069, 370759, 494345, 659127

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) >;
A120154:= func< n | g(n,9,0) >;
[A120154(n): n in [1..60]]; // G. C. Greubel, Jun 20 2023

Mathematica

A120154[n_]:= A120154[n]= 9 +Quotient[Sum[A120154[k], {k,n-1}], 3];
Table[A120154[n], {n,60}] (* G. C. Greubel, Jun 20 2023 *)

SageMath

@CachedFunction
def A120154(n): return 9 + (sum(A120154(k) for k in range(1,n)))//3
[A120154(n) for n in range(1,61)] # G. C. Greubel, Jun 20 2023