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

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

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 * A343950 A085247 A003016

Adjacent sequences: A144145 A144146 A144147 * A144149 A144150 A144151

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 11 2008

Status

approved