A119852 Number of ternary words with exactly one 012.

0, 0, 0, 1, 6, 27, 106, 387, 1350, 4566, 15102, 49113, 157622, 500520, 1575558, 4923536, 15290784, 47235771, 145246224, 444814533, 1357368786, 4128880561, 12523521786, 37888119522, 114358226428, 344437708131, 1035409733820

Offset: 0

Author

Emeric Deutsch, May 26 2006

Keywords

• nonn

Comments

Except for the initial three zeros, convolution of A076264 with itself. Column 1 of A119851.

Examples

			a(4)=6 because we have 0012, 0120, 0121, 0122, 1012 and 2012.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6, -9, -2, 6, 0, -1).

Crossrefs

Cf. A076264, A119851.

Programs

Maple

G:=z^3/(1-3*z+z^3)^2: Gser:=series(G,z=0,34): seq(coeff(Gser,z,n),n=0..30);

Mathematica

CoefficientList[Series[z^3/(1-3z+z^3)^2,{z,0,30}],z] (* or *) LinearRecurrence[ {6,-9,-2,6,0,-1},{0,0,0,1,6,27},30] (* Harvey P. Dale, Apr 28 2014 *)

Formula

G.f.=z^3/(1-3z+z^2)^2.

a(0)=0, a(1)=0, a(2)=0, a(3)=1, a(4)=6, a(5)=27, a(n)=6*a(n-1)- 9*a(n-2)- 2*a(n-3)+6*a(n-4)-a(n-6). - Harvey P. Dale, Apr 28 2014