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%I #15 Feb 13 2021 14:49:41
%S 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,
%T 35,25,18,68,97,81,71,57,40,30,20,110,157,131,115,92,65,48,33,23,178,
%U 254,212,186,149,105,78,53,38,26,288,411,343,301,241,170,126
%N Wythoff ceiling array; see Comments.
%C 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.
%F W*(n,k) = F(k+1)*ceiling(n*r) + (n - 1)*F(k), where F = A000045, the Fibonacci numbers.
%e Corner:
%e 2 4 6 10 16 26 42 68 110 178 288
%e 5 9 14 23 37 60 97 157 254 411 665
%e 7 12 19 31 50 81 131 212 343 555 898
%e 10 17 27 44 71 115 186 301 487 788 1275
%e 13 22 35 57 92 149 241 390 631 1021 1652
%e 15 25 40 65 105 170 275 445 720 1165 1885
%e 18 30 48 78 126 204 330 534 864 1398 2262
%e 20 33 53 86 139 225 364 589 953 1542 2495
%e 23 38 61 99 160 259 419 678 1097 1775 2872
%e 26 43 69 112 181 293 474 767 1241 2008 3249
%t W[n_, k_] := Fibonacci[k + 1] Ceiling[n*GoldenRatio] + (n - 1) Fibonacci[k];
%t Grid[Table[W[n, k], {n, 1, 20}, {k, 1, 18}]] (* A341260, as an array *)
%t Table[W[n - k + 1, k], {n, 12}, {k, n, 1, -1}];
%t Flatten[w] (* A341260, as a sequence *)
%Y Cf. A000045, A001950, A035513, A341261, A341262.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Feb 09 2021
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