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A239004
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Number of partitions of n having twice as many even parts as odd.
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2
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1, 0, 0, 0, 0, 1, 0, 2, 0, 4, 1, 6, 2, 9, 5, 13, 9, 18, 17, 25, 28, 35, 46, 49, 70, 70, 107, 101, 156, 145, 227, 210, 321, 303, 453, 436, 628, 622, 868, 884, 1187, 1243, 1619, 1738, 2192, 2410, 2960, 3317, 3977, 4532, 5331, 6154, 7117, 8298, 9477, 11129
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OFFSET
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0,8
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LINKS
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EXAMPLE
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a(11) counts these 6 partitions: 821, 722, 641, 632, 542, 443.
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MAPLE
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b:= proc(n, i, t) option remember;
`if`(n=0, `if`(t=0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+
`if`(i>n, 0, b(n-i, i, t+`if`(irem(i, 2)=1, 2, -1)))))
end:
a:= n-> b(n$2, 0):
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MATHEMATICA
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p[n_] := p[n] = Select[IntegerPartitions[n], 2*Count[#, _?OddQ] == Count[#, _?EvenQ] &]; Table[p[n], {n, 0, 16}] (* shows partitions *)
TableForm[t] (* partitions, vertical format *)
Table[Length[p[n]], {n, 0, 60}] (* A239004 *)
b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t + If[Mod[i, 2] == 1, 2, -1]]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Sep 01 2016, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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