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A143451
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Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=8.
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1
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1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 25, 35, 49, 67, 89, 115, 145, 179, 217, 267, 337, 435, 569, 747, 977, 1267, 1625, 2059, 2593, 3267, 4137, 5275, 6769, 8723, 11257, 14507, 18625, 23811, 30345, 38619, 49169, 62707, 80153, 102667, 131681, 168931, 216553
(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 8 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>=17, 3*a(n-17) equals the number of 3-colored compositions of n with all parts >=9, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011
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FORMULA
| G.f.: 1/(x^8*(1-x-2*x^9)).
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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(8): seq (a(n), n=0..62);
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CROSSREFS
| 8th column of A143453.
Sequence in context: A193414 A138217 A074775 * A014261 A066640 A137507
Adjacent sequences: A143448 A143449 A143450 * A143452 A143453 A143454
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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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