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 A246354 Rectangular array:  T(n,k) is the position in the infinite Fibonacci word s = A003849 at which the block s(1)..s(n) occurs for the k-th time. 2
 1, 3, 1, 4, 4, 1, 6, 6, 4, 1, 8, 9, 6, 6, 1, 9, 12, 9, 9, 6, 1, 11, 14, 12, 14, 9, 6, 1, 12, 17, 14, 19, 14, 9, 9, 1, 14, 19, 17, 22, 19, 14, 14, 9, 1, 16, 22, 19, 27, 22, 19, 22, 14, 9, 1, 17, 25, 22, 30, 27, 22, 30, 22, 14, 9, 1, 19, 27, 25, 35, 30, 27, 35 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Assuming that every row of T is infinite, each row contains the next row as a proper subsequence.  Row 1 of A246354 and row 1 of A246355 partition the positive integers. LINKS FORMULA First row: A000201 (lower Wythoff numbers); next 2 rows:  A003622 (Wythoff AA numbers); next 3 rows:  A134859 (Wythoff AAA numbers); next 5 rows:  A151915 (Wythoff AAAA numbers). (The patterns continue; in particular the number of identical consecutive rows is always a Fibonacci number, as in A000045.) EXAMPLE The lower Wythoff sequence, A000201 gives the positions of 0 in A003849, which begins thus:  0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1.  For n = 1, the block s(1)..s(1) is simply 0, which occurs at positions 1,3,4,6,8,... as in row 1 of T.  For n = 5, the block s(1)..s(5) is 0,1,0,0,1, which occurs at positions 1,6,9,14,19, ... The first 7 rows follow: 1 .. 3 .. 4 ... 6 ... 8 ... 9 ... 11 .. 12 ... 1 .. 4 .. 6 ... 9 ... 12 .. 14 .. 17 .. 19 ... 1 .. 4 .. 6 ... 9 ... 12 .. 14 .. 17 .. 19 ... 1 .. 6 .. 9 ... 14 .. 19 .. 22 .. 27 .. 30 ... 1 .. 6 .. 9 ... 14 .. 19 .. 22 .. 27 .. 30 ... 1 .. 6 .. 9 ... 14 .. 19 .. 22 .. 27 .. 30 ... 1 .. 9 .. 14 .. 22 .. 30 .. 35 .. 43 .. 48 ... MATHEMATICA z = 1000; s = Flatten[Nest[{#, #[[1]]} &, {0, 1}, 12]]; Flatten[Position[s, 0]];  b[m_, n_] := b[m, n] = Take[s, {m, n}]; z1 = 500; z2 = 12; t[k_] := t[k] = Take[Select[Range[1, z1], b[#, # + k] == b[1, 1 + k] &], z2]; Column[Table[t[k], {k, 0, z2}]] (* A246354, array *) w[n_, k_] := t[n][[k + 1]]; Table[w[n - k, k], {n, 0, z2 - 1}, {k, n, 0, -1}] // Flatten (*  A246354, sequence *) CROSSREFS Cf. A003849, A246355. Sequence in context: A276616 A286623 A246340 * A286625 A129246 A125608 Adjacent sequences:  A246351 A246352 A246353 * A246355 A246356 A246357 KEYWORD nonn,easy,tabl AUTHOR Clark Kimberling, Aug 24 2014 STATUS approved

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