A120165 - OEIS

%I #12 Sep 10 2023 09:07:53

%S 7,9,11,14,17,21,27,33,42,52,65,81,102,127,159,199,248,310,388,485,

%T 606,758,947,1184,1480,1850,2312,2890,3613,4516,5645,7056,8820,11025,

%U 13782,17227,21534,26917,33647,42058

%N a(n) = 7 + floor((1 + Sum_{j=1..n-1} a(j))/4).

%H Robert Israel, <a href="/A120165/b120165.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ c (5/4)^n with c approximately 5.5905081519. - _Robert Israel_, Mar 20 2017

%p A[1]:= 7: S:= 7:

%p for n from 2 to 100 do A[n]:= floor((29 + S)/4); S:= S + A[n] od:

%p seq(A[i],i=1..100); # _Robert Israel_, Mar 20 2017

%t a = {7}; Do[AppendTo[a, Floor[(29 + Total@ a)/4]], {i, 2, 40}]; a (* _Michael De Vlieger_, Mar 20 2017 *)

%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 A120165:= func< n | g(n, 7, 1) >;

%o [A120165(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 A120165(n): return f(n, 7, 1)

%o [A120165(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 09 2023

%Y Cf. A072493, A073941, A112088.

%Y Cf. A120160 - A120164, A120166 - A120169.

%K nonn

%O 1,1

%A _Graeme McRae_, Jun 10 2006