OFFSET
1,7
COMMENTS
The rows of the Wythoff array are essentially the positive Fibonacci sequences. If i>=1 and j>=1, then row(i+j)-row(i) is a positive Fibonacci sequence and therefore a tail of a row of the Wythoff array.
LINKS
Clark Kimberling, Antidiagonals n=1..60, flattened
EXAMPLE
Northwest corner:
1....1....1....2....1....3....2....1....4....3
1....1....1....3....1....4....2....1....6....3
1....3....1....2....1....3....8....1....4....11
1....1....1....3....1....3....2....1....4....3
1....1....2....3....1....4....2....1....6....3
Let W be the Wythoff array (A035513).
row 8 of W: 19,31,50,81,...
row 2 of W: 4,7,11,18,...
(row 8)-(row 2): 15,24,39,63,... a tail of row 4,
so that R(2,6)=4.
MATHEMATICA
w[{n_, k_}] := w[{n, k}] = Fibonacci[k + 1] Floor[n GoldenRatio] + (n - 1) Fibonacci[k];
f = Map[w[{Plus @@ #, {1, 2}}] - w[{#[[1]], {1, 2}}] &, Flatten[Table[{k, z - k + 1}, {z, 15}, {k, z}], 1]];
Module[{n, z}, Table[n = 1; While[(z = 1; While[First[f[[k]]] >= w[{n, z}], z++]); f[[k]] != {w[{n, z - 1}], w[{n, z}]}, n++]; n, {k, 1, Length[f]}]] (* Peter J. C. Moses, Apr 13 2013 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 10 2011
EXTENSIONS
Corrections and additions by Clark Kimberling, Apr 13 2013
STATUS
approved