A120158 a(n) = 14 + floor((1 + Sum_{j=1..n-1} a(j))/3).

14, 19, 25, 33, 44, 59, 79, 105, 140, 187, 249, 332, 443, 590, 787, 1049, 1399, 1865, 2487, 3316, 4421, 5895, 7860, 10480, 13973, 18631, 24841, 33122, 44162, 58883, 78511, 104681, 139575, 186100, 248133, 330844, 441125, 588167, 784223, 1045630

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) >;
A120158:= func< n | g(n, 14, 1) >;
[A120158(n): n in [1..60]]; // G. C. Greubel, Aug 31 2023

Mathematica

nxt[{a_,t_}]:=Module[{c=Floor[(43+t)/3]},{c,t+c}]; Rest[Transpose[ NestList[ nxt,{14,0},40]][[1]]] (* Harvey P. Dale, Jun 12 2014 *)
A120158[n_]:= A120158[n]= 14 +Quotient[1 +Sum[A120158[k], {k,n-1}], 3];
Table[A120158[n], {n, 60}] (* G. C. Greubel, Aug 31 2023 *)

SageMath

@CachedFunction
def A120158(n): return 14 +(1+sum(A120158(k) for k in range(1, n)))//3
[A120158(n) for n in range(1, 61)] # G. C. Greubel, Aug 31 2023