OFFSET
1,2
COMMENTS
Example: the acronyms 'OEIS' and 'SIEO' are two distinct non-palindromic words of length 4 among all possible such 456300 words (over 26 letters of the Latin alphabet).
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..705
Index entries for linear recurrences with constant coefficients, signature (26,26,-676).
FORMULA
a(n) = 2^(n/2-1)*13^(n/2)*((-1)^n*(sqrt(26)-1)-sqrt(26)-1))+26^n.
a(n) = 26^n - 26^ceiling[n/2].
G.f.: (650x)/(1 - 26x - 26x^2 + 676x^3).
a(n+3) = 26*a(n+2) + 26*a(n+1) - 676*a(n). - Robert Israel, Dec 11 2014
EXAMPLE
For n=2, the a(2)=650 solutions are {ab,ac,...,az,...,yz}, but not, e.g., 'aa' or 'zz'.
MAPLE
seq(26^n - 26^ceil(n/2), n = 1 .. 50); # Robert Israel, Dec 11 2014
MATHEMATICA
f[n_, b_] := b^n - b^Ceiling[n/2]; Array[ f[#, 26] &, 50] (* Robert G. Wilson v, Dec 10 2014 *)
Table[2^(n/2-1)*13^(n/2)*((-1)^n*(Sqrt[26]-1)-Sqrt[26]-1))+26^n, {n, 50}].
PROG
(PARI) a(n)=26^n-26^ceil(n/2) \\ Charles R Greathouse IV, Dec 10 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mikk Heidemaa, Dec 10 2014
STATUS
approved