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Search: id:A047869
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| A047869 |
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Subsets of an 8-element set in order by number of elements in each subset. |
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+0
1
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| 0, 1, 2, 4, 8, 16, 32, 64, 128, 3, 5, 6, 9, 10, 12, 17, 18, 20, 24, 33, 34, 36, 40, 48, 65, 66, 68, 72, 80, 96, 129, 130, 132, 136, 144, 160, 192, 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 67, 69, 70, 73, 74, 76, 81, 82, 84, 88, 97, 98, 100
(list; graph; listen)
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OFFSET
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8,3
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COMMENT
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Subsets are represented by binary vectors.
More generally the main diagonal of the array defined by T(0,j)=j+1 j>=0, T(i,0)=i+1 i>=0, T(i,j)=T(i-1,j-1)+T(i-1,j)+ A, is given by T(n,n)=2^(n-1)*(n+2A+2)-A - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 17 2003
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REFERENCES
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J. Loughry, Efficiently Enumerating the Subsets of a Set, submitted to ACM Trans. Math. Soft.
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FORMULA
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Main diagonal of the array defined by T(0, j)=j+1 j>=0, T(i, 0)=i+1 i>=0, T(i, j)=T(i-1, j-1)+T(i-1, j)+ 7; a(n)=2^(n-1)*(n+16)-7 - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 17 2003
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EXAMPLE
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The analogous sequences for smaller n are:
For n = 0: 0. For n = 1: 0, 1. For n = 2: 0, 1, 2, 3. For n = 3: 0, 1, 2, 4, 3, 5, 6, 7. For n = 4: 0, 1, 2, 4, 8, 3, 5, 6, 9, 10, 12, 7, 11, 13, 14, 15. For n = 5: 0, 1, 2, 4, 8, 16, 3, 5, 6, 9, 10, 12, 17, 18, 20, 24, 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 15, 23, 27, 29, 30, 31.
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CROSSREFS
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A003188.
Sequence in context: A122189 A133024 A060376 this_sequence A016025 A036161 A036159
Adjacent sequences: A047866 A047867 A047868 this_sequence A047870 A047871 A047872
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KEYWORD
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easy,fini,nonn
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AUTHOR
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Joe Loughry (loughry(AT)uswest.net)
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