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Binomial sum of compositions in standard order.
2

%I #5 Jul 24 2013 18:29:44

%S 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,

%T 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,

%U 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

%N Binomial sum of compositions in standard order.

%C The standard order of compositions is given by A066099.

%C This is the final term of the binomial transform of the composition.

%H Alois P. Heinz, <a href="/A124755/b124755.txt">Rows n = 0..14, flattened</a>

%F For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k C(k-1,i-1) b(i).

%e Composition number 11 is 2,1,1; 1*2+2*1+1*1 = 5, so a(11) = 5.

%e The table starts:

%e 0

%e 1

%e 2 2

%e 3 3 3 4

%Y Cf. A066099, A070939, A124756, A011782 (row lengths), A003462 (row sums).

%K easy,nonn,tabf

%O 0,3

%A _Franklin T. Adams-Watters_, Nov 06 2006