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A325473
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Number of compositions of n with no part divisible by 3 and an even number of parts congruent to 4 or 5 modulo 6.
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1
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1, 1, 2, 3, 5, 8, 13, 22, 38, 67, 120, 217, 395, 722, 1323, 2428, 4460, 8197, 15070, 27711, 50961, 93724, 172377, 317042, 583122, 1072519, 1972660, 3628277, 6673431, 12274342, 22576023, 41523768, 76374104, 140473865, 258371706, 475219643, 874065181, 1607656496
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (A001590(n+2) + n)/2, see Moser & Whitley reference, Theorem 3.
a(n) = A062544(n-3) + n for n >= 3 (also for n = 1 and 2 with A062544(-2) = A062544(-1) = 0), Moser & Whitney.
G.f.: (x^5-x^4+x^3-x^2+2*x-1)/((x^3+x^2+x-1)*(x-1)^2). - Alois P. Heinz, Sep 06 2019
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EXAMPLE
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a(4) counts (1,1,1,1), (1,1,2), (1,2,1), (2,1,1), (2,2), but not (1,3) or (3,1) since they contain 3, neither (4) since that has an odd number of parts congruent to 4 or 5 mod 6.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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