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A124757
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Zero-based weighted sum of compositions in standard order.
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1
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0, 0, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 3, 4, 5, 6, 0, 1, 2, 3, 3, 4, 5, 6, 4, 5, 6, 7, 7, 8, 9, 10, 0, 1, 2, 3, 3, 4, 5, 6, 4, 5, 6, 7, 7, 8, 9, 10, 5, 6, 7, 8, 8, 9, 10, 11, 9, 10, 11, 12, 12, 13, 14, 15, 0, 1, 2, 3, 3, 4, 5, 6, 4, 5, 6, 7, 7, 8, 9, 10, 5, 6, 7, 8, 8, 9, 10, 11, 9, 10, 11, 12, 12, 13, 14
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| The standard order of compositions is given by A066099.
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FORMULA
| For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k (i-1) b(i).
For n>0, a(n) = A029931(n) - A070939(n).
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EXAMPLE
| Composition number 11 is 2,1,1; 0*2+1*1+2*1 = 3, so a(11) = 3.
The table starts:
0
0
0 1
0 1 2 3
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CROSSREFS
| Cf. A066099, A070939, A029931, A011782 (row lengths), A001788 (row sums).
Sequence in context: A010873 A049804 A132387 * A049263 A014588 A053645
Adjacent sequences: A124754 A124755 A124756 * A124758 A124759 A124760
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006
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