A185735 Array by antidiagonals: R(i,j)=the number of the row of the left-justified Wythoff array W' which includes the sum of rows i and j of W'.

3, 6, 6, 4, 9, 4, 5, 7, 7, 5, 16, 21, 5, 21, 16, 7, 24, 16, 16, 24, 7, 21, 10, 19, 19, 19, 10, 21, 9, 29, 21, 22, 22, 21, 29, 9, 10, 12, 24, 24, 25, 24, 24, 12, 10, 29, 13, 10, 27, 27, 27, 27, 10, 13, 29, 12, 37, 29, 29, 30, 29

Offset

1,1

Comments

The rows of the W' array are essentially a list of all positive Fibonacci sequences. Since these sequences are closed under addition, A185735 can be viewed as an addition table.

Links

Clark Kimberling, Antidiagonals n = 1..60, flattened

Example

Let W' = left-justified Wythoff array (A165357).
  Row 1 of W':  1,0,1,1,2,3,...
  Row 2 of W':  2,1,3,4,7,11,...
  (Row 1) + (Row 2): 3,1,4,5,9,14,...
  which is Row 6, so that T(1,2)=6.
Northwest corner of A185735:
3....6....4....5....16....7
6....9....7....21...24....10
4....7....5....16...19....21
5....21...16...19...22....24
16...24...19...22...25....27

Mathematica

w[row_, k_] := Fibonacci[k + 1] Floor[row GoldenRatio] + (row - 1) Fibonacci[k]; pairs = Table[w[row, (z = 0; ((While[w[#1, z] <= w[#1, z + 1], z--]; z - 1) &)[row]) + k], {row, 600}, {k, 2}];
Flatten[Table[Position[#, #[[n - k + 1]] + #[[k]]], {n, 20}, {k, n}]] &[pairs] (* Peter J. C. Moses, Apr 07 2013 *)

Crossrefs

Cf. A035513, A165357, A165359, A165360.

Sequence in context: A105396 A247685 A372367 * A339021 A197263 A074785

Adjacent sequences: A185732 A185733 A185734 * A185736 A185737 A185738

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 02 2011

Extensions

Definition corrected by Clark Kimberling, Apr 07 2013

Status

approved