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A240146
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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 10.
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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, 42, 0, 55, 1, 75, 2, 97, 4, 128, 7, 164, 12, 212, 19, 267, 30, 340, 45, 423, 67, 530, 97, 653, 139, 807, 195, 984, 271, 1204, 370, 1456, 501, 1763, 670, 2117, 889, 2543, 1167, 3032, 1522, 3618
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OFFSET
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100,5
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COMMENTS
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With offset 110 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -10.
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LINKS
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FORMULA
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a(n) = [x^n y^10] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).
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EXAMPLE
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a(104) = 2: [23,17,15,13,11,9,7,5,3,1], [21,19,15,13,11,9,7,5,3,1].
a(125) = 2: [23,19,17,15,13,11,9,7,5,3,2,1], [21,19,17,15,13,11,9,7,5,4,3,1].
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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, -10):
seq(a(n), n=100..160);
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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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