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A119826
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Number of ternary words of length n with no 000's.
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2
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1, 3, 9, 26, 76, 222, 648, 1892, 5524, 16128, 47088, 137480, 401392, 1171920, 3421584, 9989792, 29166592, 85155936, 248624640, 725894336, 2119349824, 6187737600, 18065963520, 52746101888, 153999606016, 449623342848
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 0 of A119825.
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FORMULA
| G.f.=(1+z+z^2)/(1-2z-2z^2-2z^3).
a(n-1)=sum(m=1..n, sum(k=m..n, binomial(k-1,m-1)*sum(j=0..k, binomial(j,n-3*k+2*j)*binomial(k,j)))) [From Vladimir Kruchinin kru(AT)ie.tusur.ru Apr 25 2011]
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EXAMPLE
| a(4)=76 because among the 3^4=81 ternary words of length 4 only 0000, 0001, 0002, 1000 and 2000 contain 000's.
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MAPLE
| g:=(1+z+z^2)/(1-2*z-2*z^2-2*z^3): gser:=series(g, z=0, 32): seq(coeff(gser, z, n), n=0..28);
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PROG
| (Maxima)
a(n):=sum(sum(binomial(k-1, m-1)*sum(binomial(j, n-3*k+2*j)*binomial(k, j), j, 0, k), k, m, n), m, 1, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru Apr 25 2011]
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CROSSREFS
| Cf. A119825, A119827.
Sequence in context: A018919 A005774 A101169 * A027915 A114982 A133405
Adjacent sequences: A119823 A119824 A119825 * A119827 A119828 A119829
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), May 26 2006
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