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, 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
Offset: 1
Examples
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.
Programs
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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 *)
Comments