

A274499


Sum of the degrees of asymmetry of all ternary words of length n.


3



0, 0, 6, 18, 108, 324, 1458, 4374, 17496, 52488, 196830, 590490, 2125764, 6377292, 22320522, 66961566, 229582512, 688747536, 2324522934, 6973568802, 23245229340, 69735688020, 230127770466, 690383311398, 2259436291848, 6778308875544, 22029503845518, 66088511536554
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OFFSET

0,3


COMMENTS

The degree of asymmetry of a finite sequence of numbers is defined to be the number of pairs of symmetrically positioned distinct entries. Example: the degree of asymmetry of (2,7,6,4,5,7,3) is 2, counting the pairs (2,3) and (6,5).
A sequence is palindromic if and only if its degree of asymmetry is 0.


LINKS

Table of n, a(n) for n=0..27.


FORMULA

a(n) = (1/6)*(2n  1 + (1)^n)*3^n.
a(n) = Sum(k*A274498(n,k), k>=0).
From Chai Wah Wu, Dec 27 2018: (Start)
a(n) = 3*a(n1) + 9*a(n2)  27*a(n3) for n > 2.
G.f.: 6*x^2/((3*x  1)^2*(3*x + 1)). (End)


EXAMPLE

a(2) = 6 because the ternary words 00, 01, 02, 10, 11, 12, 20, 21, 22 have degrees of asymmetry 0, 1, 1, 1, 0, 1, 1, 1, 0, respectively.


MAPLE

a := proc (n) options operator, arrow: (1/6)*(2*n1+(1)^n)*3^n end proc: seq(a(n), n = 0 .. 30);


CROSSREFS

Cf. A274496, A274497, A274498.
Sequence in context: A280096 A009573 A052655 * A181038 A222857 A108735
Adjacent sequences: A274496 A274497 A274498 * A274500 A274501 A274502


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Jul 27 2016


STATUS

approved



