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A252700
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Number of strings of length n over a 7-letter alphabet that do not begin with a palindrome.
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9
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0, 7, 42, 252, 1722, 11802, 82362, 574812, 4021962, 28141932, 196981722, 1378789692, 9651445482, 67559543562, 472916230122, 3310409588892, 23172863100282, 162210013560042, 1135470066778362, 7948290270466812, 55638031696285962, 389466220495212042
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OFFSET
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0,2
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COMMENTS
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7 divides a(n) for all n.
lim n -> infinity a(n)/7^n ~ 0.697286015491013 is the probability that a random, infinite string over a 7-letter alphabet does not begin with a palindrome.
This sequence gives the number of walks on K_7 with loops that do not begin with a palindromic sequence.
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LINKS
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FORMULA
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EXAMPLE
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For n = 3, the first 10 of the a(3) = 252 solutions are (in lexicographic order) 011, 012, 013, 014, 015, 016, 021, 022, 023, 024.
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MATHEMATICA
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a252700[n_] := Block[{f}, f[0] = f[1] = 0;
f[x_] := 7*f[x - 1] + 7^Ceiling[(x)/2] - f[Ceiling[(x)/2]];
Prepend[Rest@Table[7^i - f[i], {i, 0, n}], 0]]; a252700[21] (* Michael De Vlieger, Dec 26 2014 *)
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PROG
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(Ruby) seq = [1, 0]; (2..N).each { |i| seq << 7 * seq[i-1] + 7**((i+1)/2) - seq[(i+1)/2] }; seq = seq.each_with_index.collect { |a, i| 7**i - a }
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CROSSREFS
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A249640 gives the number of strings of length n over a 7-letter alphabet that DO begin with a palindrome.
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KEYWORD
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easy,nonn,walk
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AUTHOR
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STATUS
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approved
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