A120153 a(n) = 7 + floor((2 + Sum_{j=1..n-1} a(j))/3).

7, 10, 13, 17, 23, 31, 41, 55, 73, 97, 130, 173, 231, 308, 410, 547, 729, 972, 1296, 1728, 2304, 3072, 4096, 5462, 7282, 9710, 12946, 17262, 23016, 30688, 40917, 54556, 72741, 96988, 129318, 172424, 229898, 306531, 408708, 544944

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) >;
A120153:= func< n | g(n,7,2) >;
[A120153(n): n in [1..60]]; // G. C. Greubel, Jun 15 2023

Mathematica

nxt[{t_,a_}]:=Module[{c=Floor[(23+t)/3]},{t+c,c}]; Rest[Transpose[ NestList[ nxt,{0,7},40]][[2]]] (* Harvey P. Dale, Oct 08 2015 *)

SageMath

@CachedFunction
def A120153(n): return 7 + (2 + sum(A120153(k) for k in range(1,n)))//3
[A120153(n) for n in range(1,61)] # G. C. Greubel, Jun 15 2023