A347068 - OEIS

%I #15 Oct 28 2021 06:31:36

%S 2,5,4,7,10,8,10,14,18,14,13,20,26,31,25,15,26,36,46,53,42,18,30,47,

%T 63,79,88,71,20,36,55,81,107,132,146,117,23,40,65,96,136,178,219,239,

%U 193,26,46,73,112,162,225,294,359,391,315,28,52,84,127,189,269

%N Rectangular array (T(n,k)), by downward antidiagonals: T(n,k) = position of k in the ordering of {h*r^m, r = 1/(golden ratio), h >= 1, 0 <= m <= n}.

%C Row 1: A001950 (upper Wythoff sequence);

%C row 2: A283234;

%C row 3: A190508;

%C col 1: A020956.

%e Corner:

%e     2,   5,   7,  10,  13,  15,  18,  20,  23, ...

%e     4,  10,  14,  20,  26,  30,  36,  40,  46, ...

%e     8,  18,  26,  36,  47,  55,  65,  73,  84, ...

%e    14,  31,  46,  63,  81,  96, 112, 127, 145, ...

%e    25,  53,  79, 107, 136, 162, 189, 215, 244, ...

%e    42,  88, 132, 178, 225, 269, 314, 358, 405, ...

%e    71, 146, 219, 294, 370, 443, 517, 590, 666, ...

%e    ...

%t z = 1000; r = N[(-1+Sqrt[5])/2];

%t s[m_] := Range[z] r^m; t[0] = s[0];

%t t[n_] := Sort[Union[s[n], t[n - 1]]]

%t row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]

%t TableForm[Table[row[n], {n, 1, 10}]] (* A347068, array *)

%t w[n_, k_] := row[n][[k]];

%t Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347068, sequence *)

%Y Cf. A001950, A020956, A283234, A190508, A347065, A347066, A347067, A347069.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Sep 02 2021