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A120926 Number of isolated 0's in all ternary words of length n on {0,1,2}. 9

%I #14 Jun 29 2023 19:09:29

%S 1,4,16,60,216,756,2592,8748,29160,96228,314928,1023516,3306744,

%T 10628820,34012224,108413964,344373768,1090516932,3443737680,

%U 10847773692,34093003032,106928054964,334731302496,1046035320300,3263630199336,10167463313316,31632108085872

%N Number of isolated 0's in all ternary words of length n on {0,1,2}.

%C This is essentially the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - 2 S); see A291000. - _Clark Kimberling_, Aug 24 2017

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -9).

%F a(n) = (4/27)*(n+1)*3^n for n >= 2.

%F G.f.: z*(1-z)^2/(1-3*z)^2.

%F a(n) = Sum_{k=0..ceiling(n/2)} k*A120924(n,k).

%e a(2) = 4 because in the 9 ternary words of length 2, namely 00, 01, 02, 10, 11, 12, 20, 21 and 22, we have altogether 4 isolated 0's.

%p 1,seq(4*(n+1)*3^n/27,n=2..28);

%Y Cf. A120924.

%K nonn

%O 1,2

%A _Emeric Deutsch_, Jul 16 2006

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)