

A144148


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


1



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, 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, 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
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OFFSET

1,3


COMMENTS

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
S(m,n)=SUM{SUM{w(i,j), i=1,2,...,m, j=1,2,...,n}.
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 array, A035513.


LINKS

Table of n, a(n) for n=1..89.


FORMULA

row 1: 1 followed by A000045
row n: (3,2,3,5,8,13,21,...) if n>1 is in the lower Wythoff sequence, A000201.
row n: (2,1,2,3,5,8,13,21,...) if n is in the upper Wythoff sequence, A001950.


EXAMPLE

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


CROSSREFS

A000045, A144112.
Sequence in context: A033178 A029418 A185736 * A085247 A003016 A328848
Adjacent sequences: A144145 A144146 A144147 * A144149 A144150 A144151


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Sep 11 2008


STATUS

approved



