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

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, 377, 377, 89, 55, 21, 5, 3, 1, 987, 987, 233, 144, 55, 13, 8, 2, 2, 2584, 2584, 610, 377, 144, 34, 21, 5, 3, 2, 6765, 6765, 1597, 987, 377, 89, 55, 13, 8, 3, 1, 17711, 17711, 4181

Offset: 1

Author

Clark Kimberling, Sep 11 2008

Keywords

• nonn
• tabl

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_{j=1..n} Sum_{i=1..m} w(i,j).

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.

Examples

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

Crossrefs

Cf. A000045, A144112, A144148.

Formula

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

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

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