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%I #3 Mar 30 2012 18:51:33
%S 1,0,1,1,0,1,2,0,0,1,2,1,0,0,1,4,2,0,0,0,1,6,3,1,0,0,0,1,9,4,2,0,0,0,
%T 0,1,14,7,3,1,0,0,0,0,1,23,10,5,2,0,0,0,0,0,1,35,17,7,3,1,0,0,0,0,0,1,
%U 55,26,11,5,2,0,0,0,0,0,0,1,87,41,17,8,3,1,0,0,0,0,0,0,1,136,64,28,11,5,2
%N As upper right triangle: ascending wiggly sums to n where first term is k (sums in which terms alternately increase and decrease; zigzag partitions).
%F If n>k>0 T(n, k)=sum_j[S(n-k, j)] over j>k and if n>0 T(n, n)=1; where S(n, k)=A059883(n, k) and if n>k>0, S(n, k)=sum_j[T(n-k, j)] over k>j (note reversal) and if n>0 S(n, n)=1.
%e Rows start (1,0,1,2,2,...), (1,0,0,1,...), (1,0,0,...) etc. T(10,4)=2 since 10 can be written as 4+6 or 4+5+1.
%Y Column sums are A025048. Cf. A025047, A025049, A059881, A059883.
%K nonn,tabl
%O 1,7
%A _Henry Bottomley_, Feb 05 2001
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