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A194922 Interspersion fractally induced by A194920, a rectangular array, by antidiagonals.

%I A194922 #10 Nov 18 2017 17:54:31
%S A194922 1,3,2,6,5,4,10,9,7,8,15,14,11,13,12,21,20,16,19,18,17,28,27,22,26,25,
%T A194922 23,24,36,35,29,34,33,30,32,31,45,44,37,43,42,38,41,40,39,55,54,46,53,
%U A194922 52,47,51,50,49,48,66,65,56,64,63,57,62,61,60,58,59,78,77,67
%N A194922 Interspersion fractally induced by A194920, a rectangular array, by antidiagonals.
%C A194922 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194922 is a permutation of the positive integers, with inverse A195071.
%H A194922 G. C. Greubel, <a href="/A194922/b194922.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%e A194922 Northwest corner:
%e A194922    1,  3,  6, 10, 15, 21
%e A194922    2,  5,  9, 14, 20, 27, 35
%e A194922    4,  7, 11, 16, 22, 29, 37
%e A194922    8, 13, 19, 26, 34, 43, 53
%e A194922   12, 18, 25, 33, 42, 52, 63
%t A194922 r = Sqrt[2]; p[n_] := n - Floor[n/r]
%t A194922 Table[p[n], {n, 1, 90}]  (* A194920 *)
%t A194922 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194922 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194922 f[20]  (* A194921 *)
%t A194922 row[n_] := Position[f[30], n];
%t A194922 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194922 v[n_, k_] := Part[row[n], k];
%t A194922 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194922 {k, 1, n}]]  (* A194922 *)
%t A194922 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194922 {n, 1, 80}]]   (* A195071 *)
%Y A194922 Cf. A194920, A194921, A195071.
%K A194922 nonn,tabl
%O A194922 1,2
%A A194922 _Clark Kimberling_, Sep 08 2011