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%I #32 Sep 19 2015 03:26:42
%S 1,2,4,6,10,16,24,34,50,72,100,138,188,254,342,454,598,784,1018,1316,
%T 1694,2166,2756,3492,4404,5530,6920,8626,10712,13264,16368,20134,
%U 24700,30212,36856,44850,54438,65918,79642,96008,115488,138642,166100,198614,237062
%N Number of binary strings of length n that avoid the pattern x x^R x (x^R is the reversal of x).
%H Giovanni Resta, <a href="/A261204/b261204.txt">Table of n, a(n) for n = 0..100</a>
%H James D. Currie, Narad Rampersad, <a href="http://arxiv.org/abs/1508.02964">Binary words avoiding x x^R x and strongly unimodal sequences</a>, arXiv:1508.02964 [math.CO], 2015.
%H James D. Currie, Narad Rampersad, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Currie/currie12.html">Binary words avoiding x x^R x and strongly unimodal sequences</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.3.
%e For n = 6, the substrings to be avoided are 000, 111, 011001, and 100110. There are 26 binary strings that avoid 000 and 111, so there are 26 - 2 = 24 binary strings of length 6 that avoid x x^R x.
%Y Cf. A028445, A241903.
%K nonn
%O 0,2
%A _Narad Rampersad_, Aug 11 2015
%E a(25)-a(44) from _Giovanni Resta_, Aug 12 2015
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