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

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

Offset: 1

Author

Emeric Deutsch, Jul 16 2006

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6, -9).

Crossrefs

Cf. A120924.

Programs

Maple

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

Formula

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

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

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