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A067693
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Minimum length of the self-conjugates partitions of n (0 if n=2; length of a partition is the number of parts).
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0
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0, 1, 0, 2, 2, 3, 3, 4, 3, 3, 4, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 5, 6, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
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OFFSET
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0,4
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COMMENTS
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There are no self-conjugate partitions of 2, so we set a(2)=0.
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LINKS
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EXAMPLE
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a(12)=4 because the self-conjugate partitions of 12 are [6,2,1,1,1,1],[5,3,2,1,1] and [4,4,2,2], having 6,5 and 4 parts, respectively; the smallest is 4.
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MAPLE
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g:=sum(t^k*x^(k^2)/product(1-t*x^(2*j), j=1..k), k=1..15): gser:=simplify(series(g, x=0, 110)): 0, 1, 0, seq(ldegree(coeff(gser, x^n)), n=3..105); # sum(t^k*x^(k^2)/product(1-t*x^(2*j), j=1..k), k=1..infinity) is the bivariate g.f. for self-conjugate partitions according to weight (i.e. sum of the parts, marked by x) and number of parts (marked by t); - Emeric Deutsch, Apr 05 2006
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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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