OFFSET
0,2
COMMENTS
10 divides a(n) for all n.
lim n -> infinity a(n)/10^n ~ 0.79111200088977 is the probability that a random, infinite string over a 10-letter alphabet does not begin with a palindrome.
This sequence gives the number of walks on K_10 with loops that do not begin with a palindromic sequence.
LINKS
Peter Kagey, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = 10^n - A249643(n) for n > 0.
EXAMPLE
For n = 3, the first 20 of the a(3) = 810 solutions are (in lexicographic order) 011, 012, 013, 014, 015, 016, 017, 018, 019, 021, 022, 023, 024, 025, 026, 027, 028, 029, 031, 032.
MATHEMATICA
a252703[n_] := Block[{f},
f[0] = f[1] = 0;
f[x_] := 10*f[x - 1] + 10^Ceiling[(x)/2] - f[Ceiling[(x)/2]];
Prepend[Rest@Table[10^i - f[i], {i, 0, n}], 0]]; a252703[20] (* Michael De Vlieger, Dec 26 2014 *)
PROG
(Ruby) seq = [1, 0]; (2..N).each { |i| seq << 10 * seq[i-1] + 10**((i+1)/2) - seq[(i+1)/2] }; seq = seq.each_with_index.collect { |a, i| 10**i - a }
CROSSREFS
KEYWORD
easy,nonn,walk
AUTHOR
Peter Kagey, Dec 20 2014
STATUS
approved