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A272727 a(0)=0; thereafter a(n+1) is the number of coincidences between the sequence so far (a(0), ..., a(n)) and its reverse (a(n), ..., a(0)).

%I A272727 #18 May 22 2016 00:25:22
%S A272727 0,1,0,3,0,3,0,5,0,7,0,7,0,7,0,9,0,9,0,11,0,13,0,15,0,15,0,15,0,15,0,
%T A272727 17,0,19,0,19,0,19,0,21,0,21,0,23,0,23,0,25,0,27,0,29,0,31,0,31,0,31,
%U A272727 0,31,0,31,0,33,0,33,0,35,0,37,0,39,0,39,0,39,0,39,0,41,0,43
%N A272727 a(0)=0; thereafter a(n+1) is the number of coincidences between  the sequence so far (a(0), ..., a(n)) and its reverse (a(n), ..., a(0)).
%C A272727 a(2n-1) is positive and odd.
%C A272727 a(2n+1) - a(2n-1) is always either 0 or 2.
%C A272727 The number of repetitions of the value 2n-1 is A272729(n).
%H A272727 Ivan Neretin, <a href="/A272727/b272727.txt">Table of n, a(n) for n = 0..8191</a>
%F A272727 a(2n)=0.
%F A272727 a(2n-1)=A272728(n)+n.
%e A272727 A one-element series [0] coincides with its own reverse, hence a(1)=1.
%e A272727 [0,1] and [1,0] differ in every term, hence a(2)=0.
%e A272727 [0,1,0] is its own reverse, hence a(3)=3.
%e A272727 [0,1,0,3] and [3,0,1,0] differ in every term, hence a(4)=0.
%e A272727 [0,1,0,3,0] and [0,3,0,1,0] coincide in three terms, hence a(5)=3.
%t A272727 Nest[Append[#, Count[# - Reverse[#], x_ /; x == 0]] &, {0}, 81]
%Y A272727 Cf. A272728, A272729.
%K A272727 nonn
%O A272727 0,4
%A A272727 _Ivan Neretin_, May 05 2016