A209869 - OEIS

%I #30 Dec 12 2023 11:27:32

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,

%T 7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,

%U 10,10,10,11,11,11,11,11,11,11,11,11,11,11

%N a(n) = a(a(n-1)) + a(n - a(n-2)) - a(a(n-3)) + a(a(n-5)), with a(1) to a(15) = 1.

%D G. Balzarotti and P. P. Lava, 103 curiosità matematiche, Hoepli, 2010, p. 275.

%D Clifford A. Pickover, The Crying of Fractal Batrachion 1,489. Chaos and Graphics, Comput. and Graphics, vol. 19, No. 4, pages 611-615, 1995.

%H Paolo P. Lava, <a href="/A209869/b209869.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = a(a(n-1)) + a(n-a(n-2)) - a(a(n-3)) + a(a(n-5)), with a(n) = 1 for n <= 15.

%F lim_{n->oo} a(n)/n = 1/4.

%p with(numtheory);

%p A209869:=proc(i)

%p local a,n;

%p a:=array(1..10000); for n from 1 to 15 do a[n]:=1; print(a[n]); od;

%p for n from 16 to i do

%p   a[n]:=a[a[n-1]]+a[n-a[n-2]]-a[a[n-3]]+a[a[n-5]]; print(a[n]);

%p od; end:

%p A209869(1000);

%t a[n_Integer] := a[n] = If[n < 16, 1, a[a[n - 1]] + a[n - a[n - 2]] - a[a[n - 3]] + a[a[n - 5]]]; Table[a[n], {n, 500}]

%K nonn

%O 1,16

%A _Paolo P. Lava_ and _Roger L. Bagula_, Mar 14 2012