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A077949
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Expansion of 1/(1-x-2*x^3).
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8
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1, 1, 1, 3, 5, 7, 13, 23, 37, 63, 109, 183, 309, 527, 893, 1511, 2565, 4351, 7373, 12503, 21205, 35951, 60957, 103367, 175269, 297183, 503917, 854455, 1448821, 2456655, 4165565, 7063207, 11976517, 20307647, 34434061, 58387095, 99002389, 167870511, 284644701
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OFFSET
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0,4
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COMMENTS
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Row sums of the Riordan array (1, x(1+2x^2)); - Paul Barry, Jan 12 2006
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>=3, 3*a(n-3) equals the number of 3-colored compositions of n with all parts >=3, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011
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LINKS
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Table of n, a(n) for n=0..38.
Index to sequences with linear recurrences with constant coefficients, signature (1,0,2)
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FORMULA
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a(n) = sum{k=0..floor(n/2), C(n-2k, k)2^k}. - Paul Barry, Nov 18 2003
a(n) = sum{k=0..n, C(k, floor((n-k)/2))2^((n-k)/2)(1+(-1)^(n-k))/2}. - Paul Barry, Jan 12 2006
a(n) = term (1,1) in the 3x3 matrix [1,1,0; 0,0,1; 2,0,0]^n. - Alois P. Heinz, Aug 16 2008
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MAPLE
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a:= n-> (<<1|1|0>, <0|0|1>, <2|0|0>>^n)[1, 1]: seq(a(n), n=0..40); # Alois P. Heinz, Aug 16 2008
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PROG
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(PARI) Vec(1/(1-x-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
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CROSSREFS
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Unsigned version of A077974. Cf. A003229.
Sequence in context: A127443 A003229 * A077974 A126273 A007658 A154321
Adjacent sequences: A077946 A077947 A077948 * A077950 A077951 A077952
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Nov 17 2002
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STATUS
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approved
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