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A238211
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The total number of 4's in all partitions of n into an odd number of distinct parts.
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2
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0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 5, 5, 6, 7, 9, 11, 13, 15, 18, 21, 25, 29, 34, 40, 46, 54, 62, 71, 82, 95, 108, 124, 142, 162, 184, 210, 238, 271, 306, 346, 392, 443, 498, 561, 632, 710, 796, 893, 1000, 1120, 1252, 1397, 1560, 1740, 1937, 2156
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OFFSET
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0,12
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COMMENTS
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The g.f. for "number of k's" is (1/2)*(x^k/(1+x^k))*(Product_{n>=1} 1 + x^n) + (1/2)*(x^k/(1-x^k))*(Product_{n>=1} 1 - x^n).
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LINKS
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FORMULA
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a(n) = Sum_{j=1..round(n/8)} A067661(n-(2*j-1)*4) - Sum_{j=1..floor(n/8)} A067659(n-8*j).
G.f.: (1/2)*(x^4/(1+x^4))*(Product{n>=1} 1 + x^n) + (1/2)*(x^4/(1-x^4))*(Product_{n>=1} 1 - x^n).
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EXAMPLE
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a(12) = 3 because the partitions in question are: 7+4+1, 6+4+2, 5+4+3.
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CROSSREFS
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KEYWORD
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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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