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A143452
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Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=9.
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1
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1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 27, 37, 51, 69, 91, 117, 147, 181, 219, 261, 315, 389, 491, 629, 811, 1045, 1339, 1701, 2139, 2661, 3291, 4069, 5051, 6309, 7931, 10021, 12699, 16101, 20379, 25701, 32283, 40421, 50523, 63141, 79003, 99045, 124443
(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 9 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>=19, 3*a(n-19) equals the number of 3-colored compositions of n with all parts >=10, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011
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FORMULA
| G.f.: 1/(x^9*(1-x-2*x^10)).
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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(9): seq (a(n), n=0..64);
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CROSSREFS
| 9th column of A143453.
Sequence in context: A158333 A062505 A093031 * A193414 A138217 A074775
Adjacent sequences: A143449 A143450 A143451 * A143453 A143454 A143455
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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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