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A090667
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Number of compositions of 3n with each part less than or equal to n.
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2
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1, 1, 13, 149, 1490, 13624, 117920, 987568, 8111200, 65866496, 531372800, 4270866688, 34254920192, 274425014272, 2197077311488, 17583865032704, 140702055981056, 1125749585477632, 9006563605151744, 72054913990721536, 576449482336632832, 4611638739487686656
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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) = 2^(3n-1)-(2n+1)*2^(2n-2)+(n+2)*(n-1)*2^(n-4), n>0.
G.f.: (896*x^6-1968*x^5+1704*x^4-757*x^3+179*x^2-21*x+1) / ((2*x-1)^3*(4*x-1)^2*(8*x-1)). - Colin Barker, May 15 2013
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EXAMPLE
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a(2)=13 since there is one composition of 6 of the form 1+1+1+1+1+1, five of the form 2+1+1+1+1, six of the form 2+2+1+1 and one of the form 2+2+2 and 1+5+6+1=13.
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MAPLE
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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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EXTENSIONS
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STATUS
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approved
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