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A194969 Interspersion fractally induced by A194968, a rectangular array, by antidiagonals.

%I A194969 #9 Oct 18 2021 08:45:27
%S A194969 1,2,3,4,6,5,7,10,8,9,11,15,12,13,14,16,21,17,18,20,19,22,28,23,24,27,
%T A194969 25,26,29,36,30,31,35,32,34,33,37,45,38,39,44,40,43,41,42,46,55,47,48,
%U A194969 54,49,53,50,51,52,56,66,57,58,65,59,64,60,61,63,62,67,78,68
%N A194969 Interspersion fractally induced by A194968, a rectangular array, by antidiagonals.
%C A194969 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194969 is a permutation of the positive integers, with inverse A194970.
%H A194969 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A194969 Northwest corner:
%e A194969 1...2...4...7...11..16
%e A194969 3...6...10..15..21..28
%e A194969 5...8...12..17..23..30
%e A194969 9...13..18..24..31..39
%e A194969 14..20..27..35..44..54
%t A194969 r = GoldenRatio; p[n_] := 1 + Floor[n/r]
%t A194969 Table[p[n], {n, 1, 90}]  (* A019446 *)
%t A194969 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194969 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194969 f[20]  (* A194968 *)
%t A194969 row[n_] := Position[f[30], n];
%t A194969 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194969 v[n_, k_] := Part[row[n], k];
%t A194969 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194969 {k, 1, n}]]  (* A194969 *)
%t A194969 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194969 {n, 1, 80}]]  (* A194970 *)
%Y A194969 Cf. A194958, A019446, A194968, A194970 (inverse).
%K A194969 nonn,tabl
%O A194969 1,2
%A A194969 _Clark Kimberling_, Sep 07 2011