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 A186007 Array by antidiagonals:  R(i,j)=number of the row of the Wythoff array which includes row(i+j)-row(i). 1
 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 3, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 4, 1, 3, 2, 1, 1, 1, 2, 3, 1, 3, 1, 1, 1, 4, 1, 8, 3, 1, 2, 1, 3, 1, 3, 6, 1, 2, 4, 1, 3, 1, 1, 1, 2, 3, 4, 1, 2, 3, 1, 2, 1, 1, 1, 5, 2, 11, 4, 1, 8 (list; table; graph; refs; listen; history; text; internal format)
 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 Cf. A035513, A185735 (addition table for Wythoff rows). Sequence in context: A051793 A065371 A300982 * A212623 A229214 A218578 Adjacent sequences:  A186004 A186005 A186006 * A186008 A186009 A186010 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Feb 10 2011 EXTENSIONS Corrections and additions by Clark Kimberling, Apr 13 2013 STATUS approved

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Last modified December 12 05:15 EST 2018. Contains 318052 sequences. (Running on oeis4.)