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A144149 Weight array W={w(i,j)} of the Wythoff difference array A080164.

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%I A144149 #6 Apr 20 2024 23:50:39
%S A144149 1,1,2,3,3,1,8,8,2,2,21,21,5,3,2,55,55,13,8,3,1,144,144,34,21,8,2,2,
%T A144149 377,377,89,55,21,5,3,1,987,987,233,144,55,13,8,2,2,2584,2584,610,377,
%U A144149 144,34,21,5,3,2,6765,6765,1597,987,377,89,55,13,8,3,1,17711,17711,4181
%N A144149 Weight array W={w(i,j)} of the Wythoff difference array A080164.
%C A144149 In general, let w(i,j) be the weight of the unit square labeled by its northeast vertex (i,j) and for each (m,n), define
%C A144149   S(m,n) = Sum_{j=1..n} Sum_{i=1..m} w(i,j).
%C A144149 Then S(m,n) is the weight of the rectangle [0,m]x[0,n]. We call W the weight array of S and we call S the accumulation array of W. For the case at hand, S is the Wythoff difference array, A080164.
%F A144149 Row 1: 1 followed by A001906, except for initial 0.
%F A144149 Row n: A001519 (except for initial 1) if n is in 1+A001950.
%F A144149 Row n: A001906 (except for initial 0) if n is in 1+A000201.
%e A144149 S(2,4) = 1+1+3+8+2+3+8+21 = 47.
%Y A144149 Cf. A000045, A144112, A144148.
%K A144149 nonn,tabl
%O A144149 1,3
%A A144149 _Clark Kimberling_, Sep 11 2008