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A251861
Number of non-palindromic words (length n>0) over the alphabet of 26 letters.
1
0, 650, 16900, 456300, 11863800, 308898200, 8031353200, 208826607600, 5429491797600, 141167083772000, 3670344178072000, 95428956352766400, 2481152865171926400, 64509974695265340800, 1677259342076898860800, 43608742899220046995200, 1133827315379721221875200, 29479510200008489360729600, 766467265200220723378969600, 19928148895209267985244544000
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).
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
Analogs for other numbers of elements: (1) A000004, (2) A233411, (3) A242278, (4) A242026, (5) A240437.
Cf. A056450.
Sequence in context: A157915 A158639 A162025 * A035851 A229797 A110836
KEYWORD
nonn,easy
AUTHOR
Mikk Heidemaa, Dec 10 2014
STATUS
approved