|
%I #6 Jan 05 2021 14:45:13
%S 1,2,4,3,7,5,6,11,9,8,10,19,15,14,12,17,31,26,23,20,13,28,51,43,39,32,
%T 22,16,46,81,71,64,53,36,27,18,75,110,101,94,83,60,44,30,21,105,138,
%U 130,123,112,90,73,49,35,24,133,165,157,151,140,119,103,79
%N Order array of the Wythoff B-array (A340244): an interspersion, read by antidiagonals.
%C Suppose that (r(n,k)), for n >= 1 and k >= 1 is an array of distinct numbers. Replace each r(n,k) with its position when all the numbers r(n,k) are ordered by <. The resulting array is the order array of (r(n,k)). The order array A340245 is an interspersion and a dispersion, and, as a sequence, a permutation of the natural numbers; see A333029 and A191450.
%e Corner:
%e 1 2 3 6 10 17 28 46
%e 4 7 11 19 31 51 81 110
%e 5 9 15 26 43 71 101 130
%e 8 14 23 39 64 94 123 151
%e 12 20 32 53 83 112 140 167
%t r = GoldenRatio; f[n_] := Fibonacci[n];
%t a[n_] := Floor[r*n]; b[n_] := Floor[r^2*n];
%t c[n_] := a[a[b[n]]]; d[n_] := b[a[b[n]]];
%t w[n_, k_] := f[k - 2] c[n] + f[k - 1] d[n];
%t Grid[Table[w[n, k], {n, 1, 9}, {k, 1, 15}]] (* A340244 array *)
%t u = Table[w[n - k + 1, k], {n, 30}, {k, n, 1, -1}]//Flatten (* A340244 sequence *)
%t rk[n_] := Position[Sort[u], u[[n]]];
%t Take[Flatten[Table[rk[n], {n, 1, 350}]], 100] (* A340245 sequence *)
%Y Cf. A191450, A333029, A340244.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Jan 02 2021
|
