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

1,3

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_{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.

Links

Table of n, a(n) for n=1..69.

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.

Example

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

Crossrefs

Cf. A000045, A144112, A144148.

Sequence in context: A323748 A116155 A365991 * A097005 A068008 A123948

Adjacent sequences: A144146 A144147 A144148 * A144150 A144151 A144152

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 11 2008

Status

approved