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A276205 a(0) = a(2) = a(3) = 0. For n>2 a(n) is the smallest nonnegative integer such that there is no arithmetic progression j,k,m,n (of length 4) such that a(j)+a(k)+a(m) = a(n).

%I A276205 #14 Aug 29 2016 18:35:26
%S A276205 0,0,0,1,0,0,2,0,0,0,1,2,1,3,0,0,0,4,0,1,2,2,3,1,4,0,0,1,0,0,0,5,3,0,
%T A276205 7,1,0,4,2,4,2,3,5,1,1,4,1,3,0,0,0,1,0,0,2,0,0,0,9,2,8,10,0,4,0,0,0,2,
%U A276205 1,7,13,4,12,4,6,7,4,4,2,0,10,2,2,1,3,1,0,0,0,12,0,9,1,0,5,2,1,17,0,3,5,0,1,1,0,0,8,3,0,0,0,15,12,9,10,11,1,5
%N A276205 a(0) = a(2) = a(3) = 0. For n>2 a(n) is the smallest nonnegative integer such that there is no arithmetic progression j,k,m,n (of length 4) such that a(j)+a(k)+a(m) = a(n).
%C A276205 This sequence, unlike A276204 (defined similarly) is seemingly irregular.
%C A276205 a(n) <= n/3. - _Robert Israel_, Aug 24 2016
%C A276205 The graph (and the definition) are reminiscent of A229037. - _N. J. A. Sloane_, Aug 29 2016
%H A276205 Michal Urbanski, <a href="/A276205/b276205.txt">Table of n, a(n) for n = 0..49999</a>
%e A276205 For n = 6 we have that:
%e A276205 a(6)>0, because a(0)+a(2)+a(4)=0 and 0,2,4,6 is an arithmetic progression.
%e A276205 a(6)>1, because a(3)+a(4)+a(5)=1 and 3,4,5,6 is an arithmetic progression.
%e A276205 there is no such arithmetic progression j,k,m,6 that a(j)+a(k)+a(m)=2, so a(6) = 2.
%p A276205 for i from 0 to 2 do A[i]:= 0 od:
%p A276205 for n from 3 to 200 do
%p A276205   Forbid:= {seq(A[n-d]+A[n-2*d]+A[n-3*d],d=1..floor(n/3))};
%p A276205   A[n]:= min({$0..max(Forbid)+1} minus Forbid)
%p A276205 od:
%p A276205 seq(A[i],i=0..200); # _Robert Israel_, Aug 24 2016
%Y A276205 Cf. A276204 (length 3), A276206 (length 5), A276207 (any length).
%Y A276205 Cf. also A229037.
%K A276205 nonn,look
%O A276205 0,7
%A A276205 _Michal Urbanski_, Aug 24 2016