%I A072705
%S A072705 1,1,0,1,2,0,1,2,0,0,1,4,0,0,0,1,4,4,0,0,0,1,6,4,0,0,0,0,1,6,8,0,0,0,0,
%T A072705 0,1,8,12,0,0,0,0,0,0,1,8,16,8,0,0,0,0,0,0,1,10,20,8,0,0,0,0,0,0,0,1,
%U A072705 10,28,16,0,0,0,0,0,0,0,0,1,12,32,24,0,0,0,0,0,0,0,0,0,1,12,40,40,0,0
%N A072705 Triangle of number of unimodal partitions/compositions of n into exactly 
               k distinct terms.
%F A072705 T(n, k) =2^(k-1)*A060016(n, k) =T(n-k, k)+2*T(n-k, k-1) [starting with 
               T(0, 0)=0, T(0, 1)=0 and T(n, 1)=1 for n>0]
%e A072705 Rows start: 1; 1,0; 1,2,0; 1,2,0,0; 1,4,0,0,0; 1,4,4,0,0,0; 1,6,4,0,0,
               0,0; 1,6,8,0,0,0,0,0; etc. T(6,3)=4 since 6 can be written as 1+2+3, 
               1+3+2, 2+3+1, or 3+2+1 but not 2+1+3 or 3+1+2.
%Y A072705 Cf. A060016, A072574, A072704. Row sums are A072706.
%Y A072705 Sequence in context: A085496 A101661 A079644 this_sequence A072574 A058650 
               A112177
%Y A072705 Adjacent sequences: A072702 A072703 A072704 this_sequence A072706 A072707 
               A072708
%K A072705 nonn,tabl
%O A072705 1,5
%A A072705 Henry Bottomley (se16(AT)btinternet.com), Jul 04 2002