A119827 Number of ternary words of length n with exactly one 000.

0, 0, 0, 1, 4, 16, 60, 212, 728, 2444, 8064, 26256, 84576, 270048, 855936, 2696080, 8446912, 26341696, 81812544, 253181888, 781005440, 2402311616, 7370247168, 22558917120, 68901651456, 210037106688, 639127277568, 1941624275200, 5889576530944, 17839902853120

Offset: 0

Author

Emeric Deutsch, May 26 2006

Keywords

• nonn
• easy

Comments

Except for the initial three zeros, convolution of A077835 with itself. Column 1 of A119825.

Examples

			a(4)=4 because we have 0001, 0002, 1000 and 2000.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,0,-4,-12,-8,-4).

Crossrefs

Cf. A077835, A119825, A119826 (without 000), A231430 (one or more 000).

Programs

Maple

h:=z^3/(1-2*z-2*z^2-2*z^3)^2: hser:=series(h,z=0,33): seq(coeff(hser,z,n), n=0..30);

Mathematica

LinearRecurrence[{4,0,-4,-12,-8,-4},{0,0,0,1,4,16},40] (* Harvey P. Dale, Jan 28 2021 *)

Formula

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