A251861 Number of non-palindromic words (length n>0) over the alphabet of 26 letters.

0, 650, 16900, 456300, 11863800, 308898200, 8031353200, 208826607600, 5429491797600, 141167083772000, 3670344178072000, 95428956352766400, 2481152865171926400, 64509974695265340800, 1677259342076898860800, 43608742899220046995200, 1133827315379721221875200, 29479510200008489360729600, 766467265200220723378969600, 19928148895209267985244544000

Offset: 1

Author

Mikk Heidemaa, Dec 10 2014

Keywords

• nonn
• easy

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).

Examples

			For n=2, the a(2)=650 solutions are {ab,ac,...,az,...,yz}, but not, e.g., 'aa' or 'zz'.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..705
• Index entries for linear recurrences with constant coefficients, signature (26,26,-676).

Crossrefs

Analogs for other numbers of elements: (1) A000004, (2) A233411, (3) A242278, (4) A242026, (5) A240437.

Cf. A056450.

Programs

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}]

PARI

a(n)=26^n-26^ceil(n/2) \\ Charles R Greathouse IV, Dec 10 2014

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.: 650*x^2/((1 - 26*x)*(1 - 26*x^2)).

a(n+3) = 26*a(n+2) + 26*a(n+1) - 676*a(n). - Robert Israel, Dec 11 2014