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