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 A349550 Meta-Wythoff array based on A097285: M = (M(n,k)), by downward antidiagonals; every row of M is eventually a row of the Wythoff array, W = A035513, and every row of W is a row of M; see Comments. 1
 1, 2, 1, 3, 3, 2, 5, 4, 3, 1, 8, 7, 5, 4, 2, 13, 11, 8, 5, 4, 3, 21, 18, 13, 9, 6, 4, 1, 34, 29, 21, 14, 10, 7, 5, 2, 55, 47, 34, 23, 16, 11, 6, 5, 3, 89, 76, 55, 37, 26, 18, 11, 7, 5, 4, 144, 123, 89, 60, 42, 29, 17, 12, 8, 5, 1, 233, 199, 144, 97, 68, 47 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Suppose that (s(1), s(2), ...) is a sequence satisfying s(k) = s(k-1) + s(k-2) for k >= 3. If s(1) and s(2) are positive integers, then there is an index n such that (s(n), s(n+1), ...) is a row of A035513. The n-th row of M is the sequence (s(1), s(2), ...), where (s(1), s(2)) are the n-th pair described in A097285. Every row of W is a row of M; indeed, M consists of all tails of all rows of W. LINKS EXAMPLE Corner: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 1, 4, 5, 9, 14, 23, 37, 60, 97, 157, 254, 411 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521 1, 5, 6, 11, 17, 28, 45, 73, 118, 191, 309, 500 2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 4, 5, 9, 14, 23, 37, 60, 97, 157, 254, 411, 665 Example: The first 7 pairs in A097285 are (1,2), (1,3), (2,3), (1,4), (2,4), (3,4), (1,5), so that the first 7 rows of M are (1,2,3,5,8,...) = (row 1 of W) = Fibonacci numbers, A000045; (1,3 4,7,11,...), which includes row 2 of W, the Lucas numbers, A000032; (2,3,5,8,13,...), a tail of row 1 of W; (1,4,5,9,14,...), which includes row 4 of W; (2,4,6,10,16,...), which includes row 3 of W; (3,4,7,11,18,...), which includes row 2 of W; (1,5,6,11,17,...), which includes row 7 of W. MATHEMATICA z1 = 30; zc = 20; zr = 20; t1 = {1, 2}; Do[t1 = Join[t1, Riffle[Range[n - 1], n], {n}], {n, 3, z1}]; (* A097285 *) t = Partition[t1, 2]; f[n_] := Fibonacci[n]; r = (1 + Sqrt[5])/2; s[h_, k_] := Table[h*f[n - 1] + k*f[n], {n, 2, zc}]; w = Table[Join[{h = t[[n]][[1]], k = t[[n]][[2]]}, s[h, k]], {n, 1, zr}] TableForm[w] (* A349550 array *) w1[n_, k_] := w[[n]][[k]]; Table[w1[n - k + 1, k], {n, 13}, {k, n, 1, -1}] // Flatten (* A349550 sequence *) CROSSREFS Cf. A000032, A000045, A035513, A097285, A349551, A349552, A349553, A349554. Sequence in context: A111492 A319254 A210864 * A144305 A138635 A128182 Adjacent sequences: A349547 A349548 A349549 * A349551 A349552 A349553 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Nov 21 2021 STATUS approved

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Last modified November 30 06:18 EST 2022. Contains 358431 sequences. (Running on oeis4.)