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%I #14 Apr 01 2018 05:57:55
%S 1,2,3,4,5,6,7,8,10,9,11,12,15,13,14,16,17,21,18,19,20,22,23,28,24,25,
%T 27,26,29,30,36,31,32,35,33,34,37,38,45,39,40,44,41,42,43,46,47,55,48,
%U 49,54,50,51,52,53,56,57,66,58,59,65,60,61,62,64,63,67,68,78,69,70,77,71,72,73,76,74,75
%N Interspersion fractally induced by A194976, 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, A194977 is a permutation of the positive integers, with inverse A194978.
%H G. C. Greubel, <a href="/A194977/b194977.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%e Northwest corner:
%e 1 2 4 7 11 16 22
%e 3 5 8 12 17 23 30
%e 6 10 15 21 28 36 45
%e 9 13 18 24 31 39 48
%e 14 19 25 32 40 49 59
%t r = Sqrt[2]; p[n_] := 1 + Floor[n/r]
%t Table[p[n], {n, 1, 90}] (* A049474 *)
%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] (* A194976 *)
%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}]] (* A194977 *)
%t q[n_] := Position[w, n]; Flatten[Table[q[n],
%t {n, 1, 80}]] (* A194978 *)
%Y Cf. A194959, A194976, A194978.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Sep 07 2011
%E Terms a(70) and beyond from _G. C. Greubel_, Mar 28 2018
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