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

0,5

Comments

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

Links

Table of n, a(n) for n=0..29.

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A121254 A261519 A262591 * A089883 A089932 A120926

Adjacent sequences: A119824 A119825 A119826 * A119828 A119829 A119830

Keyword

nonn,easy

Author

Emeric Deutsch, May 26 2006

Status

approved