login
a(n) = 11 + floor(Sum_{j-1..n-1} a(j)/4).
3

%I #7 Sep 10 2023 09:07:37

%S 11,13,17,21,26,33,41,51,64,80,100,125,156,195,244,305,381,476,595,

%T 744,930,1163,1453,1817,2271,2839,3548,4435,5544,6930,8663,10828,

%U 13535,16919,21149,26436,33045,41306,51633,64541

%N a(n) = 11 + floor(Sum_{j-1..n-1} a(j)/4).

%H G. C. Greubel, <a href="/A120168/b120168.txt">Table of n, a(n) for n = 1..1000</a>

%t f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];

%t A120168[n_]:= f[n, 11, 0];

%t Table[A120168[n], {n, 60}] (* _G. C. Greubel_, Sep 09 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)/4);

%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 A120168:= func< n | g(n, 11, 0) >;

%o [A120168(n): n in [1..60]]; // _G. C. Greubel_, Sep 09 2023

%o (SageMath)

%o @CachedFunction

%o def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4

%o def A120168(n): return f(n, 11, 0)

%o [A120168(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 09 2023

%Y Cf. A072493, A073941, A112088.

%Y Cf. A120160 - A120167, A120169.

%K nonn,easy

%O 1,1

%A _Graeme McRae_, Jun 10 2006