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A372888
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Sum of binary ranks of all strict 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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7
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0, 1, 2, 7, 13, 31, 66, 138, 279, 581, 1173, 2375, 4783, 9630, 19316, 38802, 77689, 155673, 311639, 623845, 1248179, 2497719, 4996387, 9995304, 19992908, 39990902, 79986136, 159983241, 319975073, 639971495, 1279962115, 2559966847, 5119970499, 10240030209
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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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EXAMPLE
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The strict partitions of 6 are (6), (5,1), (4,2), (3,2,1), with respective binary ranks 32, 17, 10, 7 with sum 66, so a(6) = 66.
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MAPLE
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b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, [1, 0], b(n, i-1)+ (p-> [0, p[1]*2^(i-1)]
+p)(b(n-i, min(n-i, i-1)))))
end:
a:= n-> b(n$2)[2]:
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MATHEMATICA
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Table[Total[Total[2^(#-1)]& /@ Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 0, 10}]
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CROSSREFS
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Row sums of A118462 (binary ranks of strict partitions).
For Heinz number the non-strict version is A145519, row sums of A215366.
For Heinz number (not binary rank) we have A147655, row sums of A246867.
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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