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A119827
Number of ternary words of length n with exactly one 000.
3
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.
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 26 2006
STATUS
approved