A144149 - OEIS

%I #6 Apr 20 2024 23:50:39

%S 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 377,377,89,55,21,5,3,1,987,987,233,144,55,13,8,2,2,2584,2584,610,377,

%U 144,34,21,5,3,2,6765,6765,1597,987,377,89,55,13,8,3,1,17711,17711,4181

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

%C 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   S(m,n) = Sum_{j=1..n} Sum_{i=1..m} w(i,j).

%C 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 Row 1: 1 followed by A001906, except for initial 0.

%F Row n: A001519 (except for initial 1) if n is in 1+A001950.

%F Row n: A001906 (except for initial 0) if n is in 1+A000201.

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

%Y Cf. A000045, A144112, A144148.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Sep 11 2008