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 A124755 Binomial sum of compositions in standard order. 2
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The standard order of compositions is given by A066099. This is the final term of the binomial transform of the composition. LINKS Alois P. Heinz, Rows n = 0..14, flattened FORMULA For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k C(k-1,i-1) b(i). EXAMPLE 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 CROSSREFS Cf. A066099, A070939, A124756, A011782 (row lengths), A003462 (row sums). Sequence in context: A194295 A194287 A194303 * A033810 A253272 A023965 Adjacent sequences:  A124752 A124753 A124754 * A124756 A124757 A124758 KEYWORD easy,nonn,tabf AUTHOR Franklin T. Adams-Watters, Nov 06 2006 STATUS approved

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Last modified May 15 01:35 EDT 2021. Contains 343909 sequences. (Running on oeis4.)