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A131661
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Number of compositions of n such that the cardinality of the set of parts is 2.
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4
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0, 0, 2, 5, 14, 22, 44, 68, 107, 172, 261, 396, 606, 950, 1414, 2238, 3418, 5411, 8368, 13297, 20840, 33268, 52549, 84120, 133775, 214611, 343025, 551064, 883600, 1421767, 2284870, 3680296, 5924725, 9551161, 15393855, 24834827, 40061700
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: Sum(Sum(x^(i+j)*(x^i+x^j-2)/((x^i-1)*(x^j-1)*(x^i+x^j-1)), j=1..i-1), i=2..infinity).
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MAPLE
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with(numtheory):
a:= n-> add(add(add(binomial(j+(n-i*j)/d, j), d=select(x->x<i,
divisors(n-i*j))), j=1..n/i), i=2..n-1):
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MATHEMATICA
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Rest@ CoefficientList[ Series[ Sum[ x^(i + j)*(x^i + x^j - 2)/((x^i - 1)*(x^j - 1)*(x^i + x^j - 1)), {i, 2, 37}, {j, i - 1}], {x, 0, 37}], x] (* Robert G. Wilson v, Sep 16 2007 *)
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CROSSREFS
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Cf. A242900 (with distinct multiplicities).
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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