login
Weight array W={w(i,j)} of the natural number array A038722.
0

%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