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A090868
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Number of partitions of n such that the set of odd parts has only one element.
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1
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1, 1, 3, 2, 6, 5, 11, 8, 20, 15, 32, 24, 51, 39, 80, 58, 119, 90, 175, 130, 255, 190, 361, 268, 508, 379, 706, 522, 967, 722, 1313, 974, 1771, 1317, 2363, 1754, 3131, 2330, 4123, 3058, 5388, 4010, 7001, 5200, 9053, 6731, 11631, 8642, 14878, 11068, 18944, 14076
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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_{m>0} x^(2*m-1)/(1-x^(2*m-1))/Product_{m>0} (1-x^(2*m)).
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n=0, `if`(t, 1, 0),
`if`(i<1, 0, add(b(n-i*j, i-1, t or j>0 and i::odd),
j=0..`if`(t and i::odd, 0, n/i))))
end:
a:= n-> b(n$2, false):
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MATHEMATICA
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first Needs["DiscreteMath`Combinatorica`"], then f[n_] := Count[ Plus @@@ Mod[ Union /@ Partitions[n], 2], 1]; Table[ f[n], {n, 1, 51}] (* Robert G. Wilson v, Feb 16 2004 *)
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CROSSREFS
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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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