Search: id:A144148
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%I A144148
%S A144148 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,
               2,
%T A144148 2,2,21,34,13,13,8,3,3,1,3,34,55,21,21,13,5,5,2,2,3,55,89,34,34,21,8,8,
%U A144148 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 A144148 Weight array W={w(i,j)} of the Wythoff array A035513.
%C A144148 In general, let w(i,j) be the weight of the unit square labeled by its
%C A144148 northeast vertex (i,j) and for each (m,n), define
%C A144148 S(m,n)=SUM{SUM{w(i,j), i=1,2,...,m, j=1,2,...,n}.
%C A144148 Then S(m,n) is the weight of the rectangle [0,m]x[0,n]. We call W the 
               weight
%C A144148 array of S and we call S the accumulation array of W. For the case at 
               hand, S is
%C A144148 the Wythoff array, A035513.
%F A144148 row 1: 1 followed by A000045
%F A144148 row n: (3,2,3,5,8,13,21,...) if n>1 is in the lower Wythoff sequence, 
               A000201.
%F A144148 row n: (2,1,2,3,5,8,13,21,...) if n is in the upper Wythoff sequence, 
               A001950.
%e A144148 S(2,4)=1+1+3+8+2+3+8+21=47.
%Y A144148 A000045, A144112.
%Y A144148 Sequence in context: A038575 A033178 A029418 this_sequence A085247 A003016 
               A108121
%Y A144148 Adjacent sequences: A144145 A144146 A144147 this_sequence A144149 A144150 
               A144151
%K A144148 nonn,tabl
%O A144148 1,3
%A A144148 Clark Kimberling (ck6(AT)evansville.edu), Sep 11 2008

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