login
Inverse binomial sum of compositions in standard order.
2

%I #2 Mar 30 2012 17:35:17

%S 0,1,2,0,3,1,-1,0,4,2,0,1,-2,-2,1,0,5,3,1,2,-1,-1,2,1,-3,-4,-1,-3,2,3,

%T -1,0,6,4,2,3,0,0,3,2,-2,-3,0,-2,3,4,0,1,-4,-6,-3,-6,0,0,-4,-4,3,6,2,

%U 6,-2,-4,1,0,7,5,3,4,1,1,4,3,-1,-2,1,-1,4,5,1,2,-3,-5,-2,-5,1,1,-3,-3,4,7,3,7,-1,-3,2,1,-5,-8,-5,-9,-2

%N Inverse 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 inverse binomial transform of the composition.

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

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

%e The table starts:

%e 0

%e 1

%e 2 0

%e 3 1 -1 0

%Y Cf. A066099, A124754, A124755, A011782 (row lengths), A001477 (row sums).

%K easy,sign,tabf

%O 0,3

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