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A372890
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Sum of binary ranks of all integer partitions of n, where the binary rank of a partition y is given by Sum_i 2^(y_i-1).
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8
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0, 1, 4, 10, 25, 52, 115, 228, 471, 931, 1871, 3687, 7373, 14572, 29049, 57694, 115058, 229101, 457392, 912469, 1822945, 3640998, 7277426, 14544436, 29079423, 58137188, 116254386, 232465342, 464889800, 929691662, 1859302291, 3718428513, 7436694889, 14873042016
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} 2^(k-1) * A066633(n,k).
a(n) mod 2 = A365410(n-1) for n>=1. (End)
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EXAMPLE
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The partitions of 4 are (4), (3,1), (2,2), (2,1,1), (1,1,1,1), with respective binary ranks 8, 5, 4, 4, 4 with sum 25, so a(4) = 25.
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n],
b(n, i-1)+(p->[0, p[1]*2^(i-1)]+p)(b(n-i, min(n-i, i))))
end:
a:= n-> b(n$2)[2]:
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MATHEMATICA
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Table[Total[Total[2^(#-1)]&/@IntegerPartitions[n]], {n, 0, 10}]
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CROSSREFS
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For Heinz number (not binary rank) we have A145519, row sums of A215366.
A005117 gives Heinz numbers of strict integer partitions.
A118457 lists strict partitions in Mathematica order.
A277905 groups all positive integers by binary rank of prime indices.
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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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