|
%I #12 Sep 01 2021 07:55:44
%S 1,3,1,4,3,1,6,5,3,1,8,7,5,3,1,9,9,7,5,3,1,11,11,10,7,5,3,1,12,13,12,
%T 10,7,5,3,1,14,15,14,12,10,7,5,3,1,16,17,16,15,12,10,7,5,3,1,17,19,19,
%U 17,15,12,10,7,5,3,1,19,21,21,20,17,15,12,10,7
%N Rectangular array (T(n,k)), by antidiagonals: T(n,k) = position of k in the ordering of {h/r^m, r = (1+sqrt(5))/2, h >= 1, 0 <= m <= n}.
%e Corner:
%e 1 3 4 6 8 9 11 12 14 16 17 19 21
%e 1 3 5 7 9 11 13 15 17 19 21 23 25
%e 1 3 5 7 10 12 14 16 19 21 23 25 28
%e 1 3 5 7 10 12 15 17 20 22 24 26 29
%e 1 3 5 7 10 12 15 17 20 22 24 27 30
%e 1 3 5 7 10 12 15 17 20 22 24 27 30
%e 1 3 5 7 10 12 15 17 20 22 24 27 30
%t z = 100; 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}]] (* A347065, array *)
%t w[n_, k_] := row[n][[k]];
%t Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347065, sequence *)
%Y Cf. A000201 (row 1), A005408 (row 2), A190511 (row 3), A020959 (limiting row).
%Y Cf. A347066, A347067, A347068, A347069.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Aug 16 2021
|
