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A143450
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Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=7.
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1
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1, 3, 5, 7, 9, 11, 13, 15, 17, 23, 33, 47, 65, 87, 113, 143, 177, 223, 289, 383, 513, 687, 913, 1199, 1553, 1999, 2577, 3343, 4369, 5743, 7569, 9967, 13073, 17071, 22225, 28911, 37649, 49135, 64273, 84207, 110353, 144495, 188945, 246767, 322065
(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 7 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>=15, 3*a(n-15) equals the number of 3-colored compositions of n with all parts >=8, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011
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FORMULA
| G.f.: 1/(x^7*(1-x-2*x^8)).
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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(7): seq (a(n), n=0..61);
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CROSSREFS
| 7th column of A143453.
Sequence in context: A066640 A137507 A061808 * A005842 A204458 A192861
Adjacent sequences: A143447 A143448 A143449 * A143451 A143452 A143453
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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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