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%I #3 Mar 30 2012 18:57:11
%S 1,2,1,3,1,2,4,1,1,3,5,1,1,1,4,6,1,1,1,1,5,7,1,1,1,1,1,6,8,1,1,1,1,1,
%T 1,7,9,1,1,1,1,1,1,1,8,10,1,1,1,1,1,1,1,1,9,11,1,1,1,1,1,1,1,1,1,10,
%U 12,1,1,1,1,1,1,1,1,1,1,11,13,1,1,1,1,1,1,1,1,1,1,1,12,14,1,1,1,1,1,1,1,1,1
%N Weight array W={w(i,j)} of the natural number array A038722.
%C In general, let w(i,j) be the weight of the unit square labeled by its
%C northeast vertex (i,j) and for each (m,n), define
%C S(m,n)=SUM{SUM{w(i,j), i=1,2,...,m, j=1,2,...,n}.
%C Then S(m,n) is the weight of the rectangle [0,m]x[0,n]. We call W the weight
%C array of S and we call S the accumulation array of W. For the case at hand, S is
%C the array of natural numbers having the following antidiagonals:
%C (1), then (3,2), then (6,5,4), then (10,9,8,7) and so on.
%F row 1: A000027
%F row n: n-1 followed by A000012, for n>1.
%e S(2,4)=1+1+2+3+2+1+1+1=14.
%Y A000012, A000027, A144112.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Sep 11 2008
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