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A334894 Number of maximal subsets of [n] avoiding 3-term arithmetic progressions and containing n if n>0.

%I A334894 #21 Feb 16 2025 08:34:00
%S A334894 1,1,1,2,2,1,3,6,15,4,20,7,18,6,1,3,10,29,54,123,2,16,44,170,2,31,2,
%T A334894 10,24,70,1,10,2,2,10,26,2,2,82,221,20,1,3,10,27,58,167,408,831,2005,
%U A334894 4216,14,36,106,2,6,18,30,2,2,2,8,34,2,2,4,8,12,80,211
%N A334894 Number of maximal subsets of [n] avoiding 3-term arithmetic progressions and containing n if n>0.
%H A334894 Alois P. Heinz, <a href="/A334894/b334894.txt">Table of n, a(n) for n = 0..136</a>
%H A334894 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NonaveragingSequence.html">Nonaveraging Sequence</a>
%H A334894 Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>
%H A334894 Wikipedia, <a href="https://en.wikipedia.org/wiki/Iverson_bracket">Iverson bracket</a>
%H A334894 Wikipedia, <a href="https://en.wikipedia.org/wiki/Salem-Spencer_set">Salem-Spencer set</a>
%H A334894 <a href="http://oeis.org/wiki/Index_to_OEIS:_Section_No#non_averaging">Index entries related to non-averaging sequences</a>
%F A334894 a(n) = A262347(n) - [n > 0 and A003002(n) = A003002(n-1)] * A262347(n-1).
%F A334894 a(n) = A334892(n,A003002(n)).
%F A334894 a(n) = A334187(n,A003002(n)) - [n > 0] * A334187(n-1,A003002(n)).
%Y A334894 Last elements of rows of A334892.
%Y A334894 Cf. A003002, A262347, A334187.
%K A334894 nonn
%O A334894 0,4
%A A334894 _Alois P. Heinz_, May 14 2020