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A119916
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Number of runs of 0's of odd length in all ternary words of length n.
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2
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0, 1, 4, 17, 64, 233, 820, 2825, 9568, 31985, 105796, 346913, 1129312, 3653657, 11758132, 37665881, 120172096, 382039649, 1210689028, 3825777329, 12058462720, 37918780361, 118986517684, 372650082857, 1165021837984
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n)=Sum(k*A119914(n,k),k>=0).
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 01 2010: (Start)
Binomial transform of A179608.
(End)
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FORMULA
| G.f. = z(1-z)/[(1+z)(1-3z)^2].
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 01 2010: (Start)
a(n) = ((-1)^(n-1)+(3+4*n)*3^(n-1))/8
(End)
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EXAMPLE
| a(2)=4 because in the nine ternary words of length 2, namely, 00, (0)1, (0)2,
1(0), 11, 12, 2(0), 21, 22, we have alltogether 4 runs of 0's of odd length (shown between parentheses).
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MAPLE
| g:=z*(1-z)/(1-3*z)^2/(1+z): gser:=series(g, z=0, 35): seq(coeff(gser, z, n), n=0..28);
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CROSSREFS
| Cf. A119914.
Sequence in context: A202752 A191272 A122231 * A005784 A095252 A181410
Adjacent sequences: A119913 A119914 A119915 * A119917 A119918 A119919
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), May 29 2006
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