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Search: id:A124755
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| A124755 |
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Binomial sum of compositions in standard order. |
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+0
2
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| 0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 4, 6, 5, 8, 5, 5, 5, 6, 5, 7, 6, 9, 5, 8, 7, 11, 6, 11, 9, 16, 6, 6, 6, 7, 6, 8, 7, 10, 6, 9, 8, 12, 7, 12, 10, 17, 6, 10, 9, 14, 8, 14, 12, 20, 7, 14, 12, 22, 10, 20, 17, 32, 7, 7, 7, 8, 7, 9, 8, 11, 7, 10, 9, 13, 8, 13, 11, 18, 7, 11, 10, 15, 9, 15, 13, 21, 8, 15
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The standard order of compositions is given by A066099.
This is the final term of the binomial transform of the composition.
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FORMULA
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For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k C(k-1,i-1) b(i).
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EXAMPLE
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Composition number 11 is 2,1,1; 1*2+2*1+1*1 = 5, so a(11) = 5.
The table starts:
0
1
2 2
3 3 3 4
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CROSSREFS
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Cf. A066099, A070939, A124756, A011782 (row lengths), A003462 (row sums).
Sequence in context: A034463 A071996 A072747 this_sequence A033810 A023965 A087847
Adjacent sequences: A124752 A124753 A124754 this_sequence A124756 A124757 A124758
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006
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