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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 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 May 25 19:30 EDT 2020. Contains 334595 sequences. (Running on oeis4.)