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A240145
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Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 9.
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2
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1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 11, 0, 15, 0, 22, 0, 30, 0, 41, 1, 54, 2, 73, 4, 94, 7, 123, 12, 157, 19, 201, 30, 252, 45, 318, 67, 393, 97, 488, 139, 598, 194, 732, 269, 888, 366, 1078, 494, 1296, 658, 1558, 870, 1862, 1137, 2222, 1477, 2639, 1900, 3133
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OFFSET
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81,5
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COMMENTS
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With offset 90 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -9.
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LINKS
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FORMULA
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a(n) = [x^n y^9] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).
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EXAMPLE
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a(87) = 3: [23,15,13,11,9,7,5,3,1], [21,17,13,11,9,7,5,3,1], [19,17,15,11,9,7,5,3,1].
a(102) = 1: [19,17,15,13,11,9,7,5,3,2,1].
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2 or
abs(t)>n, 0, `if`(n=0, 1, b(n, i-1, t)+
`if`(i>n, 0, b(n-i, i-1, t+(2*irem(i, 2)-1)))))
end:
a:= n-> b(n$2, -9):
seq(a(n), n=81..145);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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