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A007055
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Let S denote the palindromes in the language {0,1}*; a(n) = number of words of length n in the language SS.
(Formerly M1124)
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6
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1, 2, 4, 8, 16, 32, 52, 100, 160, 260, 424, 684, 1036, 1640, 2552, 3728, 5920, 8672, 13408, 19420, 30136, 42736, 66840, 94164, 145900, 204632, 317776, 441764, 685232, 950216, 1469632, 2031556, 3139360, 4323888, 6675904, 9174400, 14139496, 19398584, 29864888, 40891040, 62882680, 85983152
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of words in {0,1}* of length n that are rotations of their reversals. - David W. Wilson, Jan 01 2012.
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REFERENCES
| R. Kemp, On the number of words in the language {w in Sigma* | w = w^R }^2, Discrete Math., 40 (1982), 225-234.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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MAPLE
| # A023900:
f:=proc(n) local t0, t1, t2; if n=1 then RETURN(1) else
t0:=1; t1:=ifactors(n); t2:=t1[2]; for i from 1 to nops(t2) do t0:=t0*(1-t2[i][1]); od; RETURN(t0); fi; end;
# A187272-A187275:
R:=(a, n)->
expand(simplify( (n/4)*a^(n/2)*( (1+sqrt(a))^2+ (-1)^n*(1-sqrt(a))^2 ) ));
# A007055, A007056, A007057, A007058
F:=(b, n)-> if n=0 then 1 else expand(simplify( add( f(d)*R(b, n/d), d in divisors(n) ) )); fi;
# A007055:
[seq(F(2, n), n=0..60)];
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CROSSREFS
| Cf. A007056-A007058, A023900, A187272-A187275.
Sequence in context: A133408 A101434 A008382 * A072207 A175951 A176718
Adjacent sequences: A007052 A007053 A007054 * A007056 A007057 A007058
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, R. Kemp
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EXTENSIONS
| Entry revised by N. J. A. Sloane, Mar 07 2011
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