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A258259
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Number of partitions of n into distinct parts less than or equal to n/2.
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5
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1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 3, 2, 5, 4, 8, 8, 13, 13, 21, 21, 31, 33, 46, 49, 67, 72, 95, 104, 134, 146, 186, 203, 253, 279, 343, 378, 461, 507, 611, 675, 806, 889, 1055, 1163, 1369, 1512, 1768, 1950, 2270, 2502, 2896, 3193, 3678, 4051, 4649, 5117, 5847
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OFFSET
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0,11
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COMMENTS
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Intuitively the sequence is asymptotic to A000009. a(300)/A000009(300) is approximately .997749.
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LINKS
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FORMULA
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a(n) = [x^n] Product_{i=1..floor(n/2)} 1 + x^i.
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EXAMPLE
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a(9) = 1 because we have: 2+3+4.
a(10) = 3 because we have: 1+4+5, 2+3+5, 1+2+3+4.
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MAPLE
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b:= proc(n, i) option remember; local m; m:= i*(i+1)/2;
`if`(n>m, 0, `if`(n=m, 1, b(n, i-1)+`if`(i>n, 0, b(n-i, i-1))))
end:
a:= n-> b(n, iquo(n, 2)):
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MATHEMATICA
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Prepend[Table[nn = n; Coefficient[Series[Product[1 + x^i, {i, 1, nn/2}], {x, 0, nn}], x^n], {n, 1, 50}], 1]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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