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Search: id:A116665
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| A116665 |
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Total number of parts that appear exactly once in the partitions of n into odd parts. |
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+0
2
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| 0, 1, 0, 1, 2, 2, 3, 4, 6, 7, 10, 12, 16, 20, 25, 31, 39, 47, 58, 71, 85, 103, 124, 148, 176, 210, 248, 293, 345, 405, 474, 555, 645, 751, 872, 1009, 1166, 1346, 1549, 1781, 2044, 2341, 2678, 3060, 3488, 3973, 4520, 5132, 5822, 6597, 7464, 8436, 9525, 10740
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OFFSET
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0,5
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COMMENT
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a(n)=Sum(k*A116664(n,k),k>=0).
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FORMULA
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G.f.=x(1-x+x^2)/[(1-x^4)product(1-x^(2j-1), j=1..infinity)].
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EXAMPLE
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a(8)=6 because in the partitions of 8 into odd parts, namely, [(7),(1)],[(5),(3)],[(5),1,1,1],[3,3,1,1],[(3),1,1,1,1,1], and [1,1,1,1,1,1,1,1], we have 6 parts that appear exactly once (shown between parentheses).
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MAPLE
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f:=x*(1-x+x^2)/(1-x^4)/product(1-x^(2*j-1), j=1..40): fser:=series(f, x=0, 61): seq(coeff(fser, x, n), n=0..57);
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CROSSREFS
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Cf. A116664.
Sequence in context: A102464 A082538 A035939 this_sequence A122135 A027194 A039883
Adjacent sequences: A116662 A116663 A116664 this_sequence A116666 A116667 A116668
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
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