1,2

D is an interspersion formed by differences between Wythoff pairs in the Wythoff array W={w(i,j)}=A035513 (indexed so that i and j start at 1): d(i,j)=w(i,2j)-w(i,2j-1).

The difference between adjacent column terms is a Fibonacci number: d(i+1,j)-d(i,j) is F(2j) or F(2j+1).

Every term in column 1 of W is in column 1 of D and in row i of D, every term except the first is in row i of W.

Let W' be the array remaining when all the odd-numbered columns of W are removed from W. The rank array of W' (obtained by replacing each w'(i,j) by its rank when all the numbers w'(h,k) are arranged in increasing order) is D.

Let W" be the array remaining when all the even-numbered columns of W are removed from W; the rank array of W" is D.

Let D' be the array remaining when column 1 of D is removed; the rank array of D' is D.

Let E be the array {e(i,j)} given by e(i,j)=d(i,2j)-d(i,2j-1); the rank array of E is D.

C. Kimberling, The Wythoff difference array, preprint, 2003.

Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

C. Kimberling, Interspersions

Index entries for sequences that are permutations of the natural numbers

d(i, j)=[i*tau]F(2j-1)+(i-1)F(2j-2), where F=A000045 (Fibonacci numbers). d(i, j)=[tau*d(i, j-1)]+d(i, j-1) for i>=2. d(i, j)=3d(i, j-1)-d(i, j-2) for i>=3.

Northwest corner:

1 2 5 13

3 7 18 47

4 10 26 68

6 15 39 102

8 20 52 136

Cf. A035513, A000201, A001950.

Sequence in context: A103683 A125151 A103866 this_sequence A126048 A142349 A081622

Adjacent sequences: A080161 A080162 A080163 this_sequence A080165 A080166 A080167

nonn,tabl

Clark Kimberling (ck6(AT)evansville.edu), Feb 08 2003