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%I #13 Mar 24 2017 00:47:57
%S 0,9,72,576,5112,45432,408312,3669696,33022152,297153936,2674339992,
%T 24068651616,216617456232,1949553436392,17545977257832,
%U 157913762298336,1421223827662872,12791014151811912,115119127069153272,1036072140948039456,9324649265858015112
%N Number of strings of length n over a 9-letter alphabet that do not begin with a palindrome.
%C 9 divides a(n) for all n.
%C lim n -> infinity a(n)/9^n ~ 0.766976957370438 is the probability that a random, infinite string over a 9-letter alphabet does not begin with a palindrome.
%C This sequence gives the number of walks on K_9 with loops that do not begin with a palindromic sequence.
%H Peter Kagey, <a href="/A252702/b252702.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = 9^n - A249642(n) for n > 0.
%e For n = 3, the first 10 of the a(3) = 576 solutions are (in lexicographic order) 011, 012, 013, 014, 015, 016, 017, 018, 021, 022.
%o (Ruby) seq = [1, 0]; (2..N).each { |i| seq << 9 * seq[i-1] + 9**((i+1)/2) - seq[(i+1)/2] }; seq = seq.each_with_index.collect { |a, i| 9**i - a }
%Y A249642 gives the number of strings of length n over a 9-letter alphabet that DO begin with a palindrome.
%Y Analogous sequences for k-letter alphabets: A252696 (k=3), A252697 (k=4), A252698 (k=5), A252699 (k=6), A252700 (k=7), A252701 (k=8), A252703 (k=10).
%K easy,nonn,walk
%O 0,2
%A _Peter Kagey_, Dec 20 2014
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