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A341260
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Wythoff ceiling array; see Comments.
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3
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2, 4, 5, 6, 9, 7, 10, 14, 12, 10, 16, 23, 19, 17, 13, 26, 37, 31, 27, 22, 15, 42, 60, 50, 44, 35, 25, 18, 68, 97, 81, 71, 57, 40, 30, 20, 110, 157, 131, 115, 92, 65, 48, 33, 23, 178, 254, 212, 186, 149, 105, 78, 53, 38, 26, 288, 411, 343, 301, 241, 170, 126
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OFFSET
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1,1
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COMMENTS
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The Wythoff array, A035513, is given by W(n,k) = F(k+1)*floor(n*r) + (n - 1)*F(k), where F = A000045, the Fibonacci numbers. The Wythoff ceiling array, W*, is defined by W*(n,k) = F(k+1)*ceiling(n*r) + (n - 1)*F(k). This is a subarray of W; viz., row n of W* is row A001950(n) + 1 of the extended Wythoff array shown at A035513. Column 1: A001950 (upper Wythoff sequence). Some numbers, as in A341261, occur twice in W*, but none occurs more than twice. The set of numbers not in W* is given by A341262.
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LINKS
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FORMULA
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W*(n,k) = F(k+1)*ceiling(n*r) + (n - 1)*F(k), where F = A000045, the Fibonacci numbers.
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EXAMPLE
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Corner:
2 4 6 10 16 26 42 68 110 178 288
5 9 14 23 37 60 97 157 254 411 665
7 12 19 31 50 81 131 212 343 555 898
10 17 27 44 71 115 186 301 487 788 1275
13 22 35 57 92 149 241 390 631 1021 1652
15 25 40 65 105 170 275 445 720 1165 1885
18 30 48 78 126 204 330 534 864 1398 2262
20 33 53 86 139 225 364 589 953 1542 2495
23 38 61 99 160 259 419 678 1097 1775 2872
26 43 69 112 181 293 474 767 1241 2008 3249
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MATHEMATICA
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W[n_, k_] := Fibonacci[k + 1] Ceiling[n*GoldenRatio] + (n - 1) Fibonacci[k];
Grid[Table[W[n, k], {n, 1, 20}, {k, 1, 18}]] (* A341260, as an array *)
Table[W[n - k + 1, k], {n, 12}, {k, n, 1, -1}];
Flatten[w] (* A341260, as a sequence *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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