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A143449
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Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=6.
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1
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1, 3, 5, 7, 9, 11, 13, 15, 21, 31, 45, 63, 85, 111, 141, 183, 245, 335, 461, 631, 853, 1135, 1501, 1991, 2661, 3583, 4845, 6551, 8821, 11823, 15805, 21127, 28293, 37983, 51085, 68727, 92373, 123983, 166237, 222823, 298789, 400959, 538413, 723159, 971125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is also the number of length n ternary words with at least 6 0-digits between any other digits.
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=13, 3*a(n-13) equals the number of 3-colored compositions of n with all parts >=7, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011
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FORMULA
| G.f.: 1/(x^6*(1-x-2*x^7)).
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MAPLE
| a := proc(k::nonnegint) local n, i, j; if k=0 then unapply (3^n, n) else unapply ((Matrix(k+1, (i, j)-> if (i=j-1) or j=1 and i=1 then 1 elif j=1 and i=k+1 then 2 else 0 fi)^(n+k))[1, 1], n) fi end(6): seq (a(n), n=0..58);
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CROSSREFS
| 6th column of A143453.
Sequence in context: A192861 A192868 A081110 * A033034 A185189 A184591
Adjacent sequences: A143446 A143447 A143448 * A143450 A143451 A143452
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 16 2008
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