

A120926


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


8



1, 4, 16, 60, 216, 756, 2592, 8748, 29160, 96228, 314928, 1023516, 3306744, 10628820, 34012224, 108413964, 344373768, 1090516932, 3443737680, 10847773692, 34093003032, 106928054964, 334731302496, 1046035320300, 3263630199336, 10167463313316, 31632108085872
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OFFSET

1,2


COMMENTS

This is essentially the pINVERT of (1,1,1,1,1,...) for p(S) = (1  2 S); see A291000.  Clark Kimberling, Aug 24 2017


LINKS

Table of n, a(n) for n=1..27.


FORMULA

a(n) = (4/27)*(n+1)*3^n for n >= 2.
G.f.: z*(1z)^2/(13*z)^2.
a(n) = Sum_{k=0..ceiling(n/2)} k*A120924(n,k).


EXAMPLE

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.


MAPLE

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


CROSSREFS

Cf. A120924.
Sequence in context: A119827 A089883 A089932 * A255303 A273347 A268939
Adjacent sequences: A120923 A120924 A120925 * A120927 A120928 A120929


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Jul 16 2006


STATUS

approved



