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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 (list; graph; refs; listen; history; text; internal format)
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(n-1) + 9*a(n-2) - 27*a(n-3) 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*n-1+(-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

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)