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A238213
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The total number of 6'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, 0, 0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 17, 20, 23, 27, 33, 38, 44, 51, 59, 68, 79, 91, 104, 119, 136, 155, 178, 202, 230, 261, 296, 335, 379, 428, 483, 544, 612, 688, 773, 867, 972, 1088, 1217, 1360, 1518, 1693, 1887
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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/12)} A067661(n-(2*j-1)*6) - Sum_{j=1..floor(n/12)} A067659(n-12*j).
G.f.: (1/2)*(x^6/(1+x^6))*(Product_{n>=1} 1 + x^n) + (1/2)*(x^6/(1-x^6))*(Product_{n>=1} 1 - x^n).
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EXAMPLE
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a(12) = 2 because the partitions in question are: 6+5+1, 6+4+2.
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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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