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

0,5

Comments

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

Links

Table of n, a(n) for n=0..26.

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

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

Example

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

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 *)

Crossrefs

Cf. A076264, A119851.

Sequence in context: A000395 A005325 A099623 * A220529 A027471 A305780

Adjacent sequences: A119849 A119850 A119851 * A119853 A119854 A119855

Keyword

nonn

Author

Emeric Deutsch, May 26 2006

Status

approved