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A370819
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Number of subsets of {1..n-1} whose cardinality is one less than the length of the binary expansion of n; a(0) = 0.
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1
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0, 1, 1, 2, 3, 6, 10, 15, 35, 56, 84, 120, 165, 220, 286, 364, 1365, 1820, 2380, 3060, 3876, 4845, 5985, 7315, 8855, 10626, 12650, 14950, 17550, 20475, 23751, 27405, 169911, 201376, 237336, 278256, 324632, 376992, 435897, 501942, 575757, 658008, 749398, 850668
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = binomial(n - 1, A029837(n+1) - 1) = binomial(n - 1, A113473(n) - 1) = binomial(n - 1, A070939(n) - 1) for n > 0.
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EXAMPLE
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The a(1) = 1 through a(7) = 15 subsets:
{} {1} {1} {1,2} {1,2} {1,2} {1,2}
{2} {1,3} {1,3} {1,3} {1,3}
{2,3} {1,4} {1,4} {1,4}
{2,3} {1,5} {1,5}
{2,4} {2,3} {1,6}
{3,4} {2,4} {2,3}
{2,5} {2,4}
{3,4} {2,5}
{3,5} {2,6}
{4,5} {3,4}
{3,5}
{3,6}
{4,5}
{4,6}
{5,6}
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MATHEMATICA
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Table[If[n==0, 0, Binomial[n-1, IntegerLength[n, 2]-1]], {n, 0, 15}]
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CROSSREFS
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The version without subtracting one is A357812.
A007318 counts subsets by cardinality.
A070939 gives length of binary expansion.
A096111 gives product of binary 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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