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A144148 Weight array W={w(i,j)} of the Wythoff array A035513. 1


%S 1,1,3,1,2,2,2,3,1,3,3,5,2,2,3,5,8,3,3,2,2,8,13,5,5,3,1,3,13,21,8,8,5,

%T 2,2,2,21,34,13,13,8,3,3,1,3,34,55,21,21,13,5,5,2,2,3,55,89,34,34,21,

%U 8,8,3,3,2,2,89,144,55,55,34,13,13,5,5,3,1,3,144,233,89,89,55,21,21,8,8,8,5

%N Weight array W={w(i,j)} of the Wythoff array A035513.

%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 Wythoff array, A035513.

%F row 1: 1 followed by A000045

%F row n: (3,2,3,5,8,13,21,...) if n>1 is in the lower Wythoff sequence, A000201.

%F row n: (2,1,2,3,5,8,13,21,...) if n is in the upper Wythoff sequence, A001950.

%e S(2,4)=1+1+3+8+2+3+8+21=47.

%Y A000045, A144112.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Sep 11 2008

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