A185735 - OEIS

%I #18 Feb 12 2014 18:14:19

%S 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,

%T 21,9,29,21,22,22,21,29,9,10,12,24,24,25,24,24,12,10,29,13,10,27,27,

%U 27,27,10,13,29,12,37,29,29,30,29

%N 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'.

%C 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.

%H Clark Kimberling, <a href="/A185735/b185735.txt">Antidiagonals n = 1..60, flattened</a>

%e Let W' = left-justified Wythoff array (A165357).

%e   Row 1 of W':  1,0,1,1,2,3,...

%e   Row 2 of W':  2,1,3,4,7,11,...

%e   (Row 1) + (Row 2): 3,1,4,5,9,14,...

%e   which is Row 6, so that T(1,2)=6.

%e Northwest corner of A185735:

%e 3....6....4....5....16....7

%e 6....9....7....21...24....10

%e 4....7....5....16...19....21

%e 5....21...16...19...22....24

%e 16...24...19...22...25....27

%t 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}];

%t Flatten[Table[Position[#, #[[n - k + 1]] + #[[k]]], {n, 20}, {k, n}]] &[pairs] (* _Peter J. C. Moses_, Apr 07 2013 *)

%Y Cf. A035513, A165357, A165359, A165360.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Feb 02 2011

%E Definition corrected by _Clark Kimberling_, Apr 07 2013