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A143448
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Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=5.
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2
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1, 3, 5, 7, 9, 11, 13, 19, 29, 43, 61, 83, 109, 147, 205, 291, 413, 579, 797, 1091, 1501, 2083, 2909, 4067, 5661, 7843, 10845, 15011, 20829, 28963, 40285, 55971, 77661, 107683, 149341, 207267, 287837, 399779, 555101, 770467, 1069149, 1483683
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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>=11, 3*a(n-11) equals the number of 3-colored compositions of n with all parts >=6, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011
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FORMULA
| G.f.: 1/(x^5*(1-x-2*x^6)).
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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(5): seq (a(n), n=0..56);
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CROSSREFS
| 5th column of A143453.
Sequence in context: A172095 A133854 A030155 * A039786 A130738 A024323
Adjacent sequences: A143445 A143446 A143447 * A143449 A143450 A143451
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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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