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A304590 a(1) = a(2) = a(3) = a(5) = 1, a(4) = 2, a(6) = 3; a(n) = a(n-a(n-3)) + a(n-a(n-6)) for n > 6.

%I A304590 #14 Aug 07 2018 06:56:41
%S A304590 1,1,1,2,1,3,4,8,11,11,12,12,12,4,3,3,13,6,7,7,9,10,14,9,9,19,12,13,
%T A304590 14,15,16,18,15,15,22,18,19,10,18,18,23,18,18,24,24,26,23,24,30,31,24,
%U A304590 29,25,30,28,25,27,29,30,30,33,37,33,38,35,33,29,31,36,41,36,36,42,28,36,37,53,36,37,41,48,48,33
%N A304590 a(1) = a(2) = a(3) = a(5) = 1, a(4) = 2, a(6) = 3; a(n) = a(n-a(n-3)) + a(n-a(n-6)) for n > 6.
%H A304590 Altug Alkan, <a href="/A304590/b304590.txt">Table of n, a(n) for n = 1..10000</a>
%p A304590 f:= proc(n) option remember; procname(n-procname(n-3))+procname(n-procname(n-6)) end proc:
%p A304590 for i from 1 to 6 do f(i):= [1,1,1,2,1,3][i] od:
%p A304590 map(f, [$1..100]); # _Robert Israel_, May 16 2018
%t A304590 Nest[Append[#2, #2[[#1 - #2[[-3]] ]] + #2[[#1 - #2[[-6]] ]] ] & @@ {Length@ # + 1, #} &, {1, 1, 1, 2, 1, 3}, 77] (* _Michael De Vlieger_, Jul 20 2018 *)
%o A304590 (PARI) q=vector(100); q[1]=q[2]=q[3]=q[5]=1;q[4]=2;q[6]=3; for(n=7, #q, q[n]=q[n-q[n-3]]+q[n-q[n-6]]); q
%o A304590 (GAP) a:=[1,1,1,2,1,3];; for n in [7..100] do a[n]:=a[n-a[n-3]]+a[n-a[n-6]]; od; a; # _Muniru A Asiru_, May 19 2018
%Y A304590 Cf. A005185, A063882, A087777, A240827.
%K A304590 nonn
%O A304590 1,4
%A A304590 _Altug Alkan_, May 15 2018