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A267306 Earliest nonnegative increasing sequence having no 6-term subsequence with constant third differences.

%I A267306 #9 Jan 01 2021 11:37:25
%S A267306 0,1,2,3,4,6,7,8,9,11,12,13,14,28,29,31,32,33,34,35,37,38,40,47,79,93,
%T A267306 94,96,97,98,99,100,102,103,105,110,116,122,128,130,140,148,266,281,
%U A267306 296,303,304,306,308,311,313,318,324,326,327,328,330,331,332,337
%N A267306 Earliest nonnegative increasing sequence having no 6-term subsequence with constant third differences.
%o A267306 (PARI) A267306(n, show=0, L=6, o=3, v=[0], D=v->v[2..-1]-v[1..-2])={ my(d, m); while( #v<n, show&&print1(v[#v]", "); v=concat(v, v[#v]); while( v[#v]++, forvec( i=vector(L, j, [if(j<L, j, #v), #v]), d=D(vecextract(v, i)); m=o; while(m--&&#Set(d=D(d))>1, ); #Set(d)>1||next(2), 2); break)); v[#v]} \\ _M. F. Hasler_, Jan 12 2016
%Y A267306 Cf. A267307 (positive variant: starting with 1).
%Y A267306 No 3-term AP: A005836 (>=0), A003278 (>0);
%Y A267306 no 4-term AP: A240075 (>=0), A240555 (>0);
%Y A267306 no 5-term AP: A020654 (>=0), A020655 (>0);
%Y A267306 no 6-term AP: A020656 (>=0), A005838 (>0);
%Y A267306 no 7-term AP: A020657 (>=0), A020658 (>0);
%Y A267306 no 8-term AP: A020659 (>=0), A020660 (>0);
%Y A267306 no 9-term AP: A020661 (>=0), A020662 (>0);
%Y A267306 no 10-term AP: A020663 (>=0), A020664 (>0).
%Y A267306 Cf. A240075 and A240555 for sequences avoiding 4-term subsequences with constant second differences.
%Y A267306 Cf. A267300 and A267301 for sequences avoiding 5-term subsequences with constant second differences.
%Y A267306 Cf. A267302 and A267303 for sequences avoiding 6-term subsequences with constant second differences.
%Y A267306 Cf. A267304 and A267305 for sequences avoiding 7-term subsequences with constant second differences.
%Y A267306 Cf. A240556 and A240557 for sequences avoiding 5-term subsequences with constant third differences.
%K A267306 nonn
%O A267306 1,3
%A A267306 _M. F. Hasler_, Jan 12 2016
%E A267306 More terms from _Jinyuan Wang_, Jan 01 2021