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A240011
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Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 2.
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2
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1, 0, 1, 1, 2, 2, 3, 4, 5, 8, 8, 13, 14, 21, 23, 34, 37, 52, 60, 79, 93, 120, 143, 178, 216, 263, 321, 386, 470, 560, 684, 806, 980, 1154, 1395, 1636, 1969, 2304, 2758, 3225, 3835, 4480, 5305, 6186, 7288, 8495, 9961, 11594, 13545, 15742, 18325, 21269, 24675
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OFFSET
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2,5
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COMMENTS
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With offset 4 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -2.
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LINKS
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EXAMPLE
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a(10) = 5: [9,1], [7,3], [5,5], [4,2,1,1,1,1], [3,2,2,1,1,1].
a(11) = 8: [8,1,1,1], [7,2,1,1], [6,3,1,1], [5,4,1,1], [5,3,2,1], [4,3,3,1], [3,3,3,2], [2,2,2,1,1,1,1,1].
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MAPLE
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b:= proc(n, i, t) option remember; `if`(abs(t)>n, 0,
`if`(n=0, 1, `if`(i<1, 0, b(n, i-1, t)+
`if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1))))))
end:
a:= n-> b(n$2, -2):
seq(a(n), n=2..80);
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[Abs[t] > n, 0, If[n == 0, 1, If[i < 1, 0, b[n, i - 1, t] + If[i > n, 0, b[n - i, i, t + 2 Mod[i, 2] - 1]]]]];
a[n_] := b[n, n, -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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STATUS
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approved
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