login
a(n) = 15 + floor((2 + Sum_{j=1..n-1} a(j))/3).
1

%I #7 Sep 01 2023 04:16:53

%S 15,20,27,36,48,64,85,114,152,202,270,360,480,640,853,1137,1516,2022,

%T 2696,3594,4792,6390,8520,11360,15146,20195,26927,35902,47870,63826,

%U 85102,113469,151292,201723,268964,358618,478158,637544,850058,1133411

%N a(n) = 15 + floor((2 + Sum_{j=1..n-1} a(j))/3).

%H G. C. Greubel, <a href="/A120159/b120159.txt">Table of n, a(n) for n = 1..1000</a>

%t A120159[n_]:= A120159[n]= 15 +Quotient[2 +Sum[A120159[k], {k,n-1}], 3];

%t Table[A120159[n], {n, 60}] (* _G. C. Greubel_, Aug 31 2023 *)

%o (Magma)

%o function f(n, a, b)

%o t:=0;

%o for k in [1..n-1] do

%o t+:= a+Floor((b+t)/3);

%o end for;

%o return t;

%o end function;

%o g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;

%o A120159:= func< n | g(n, 15, 2) >;

%o [A120159(n): n in [1..60]]; // _G. C. Greubel_, Aug 31 2023

%o (SageMath)

%o @CachedFunction

%o def A120159(n): return 15 +(2+sum(A120159(k) for k in range(1, n)))//3

%o [A120159(n) for n in range(1, 61)] # _G. C. Greubel_, Aug 31 2023

%Y Cf. A072493, A073941, A112088.

%K nonn,easy

%O 1,1

%A _Graeme McRae_, Jun 10 2006

%E Name edited by _G. C. Greubel_, Aug 31, 2023