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A194977 Interspersion fractally induced by A194976, a rectangular array, by antidiagonals.

%I A194977 #14 Apr 01 2018 05:57:55
%S A194977 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 A194977 27,26,29,30,36,31,32,35,33,34,37,38,45,39,40,44,41,42,43,46,47,55,48,
%U A194977 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 A194977 Interspersion fractally induced by A194976, a rectangular array, by antidiagonals.
%C A194977 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 A194977 G. C. Greubel, <a href="/A194977/b194977.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%e A194977 Northwest corner:
%e A194977    1  2  4  7 11 16 22
%e A194977    3  5  8 12 17 23 30
%e A194977    6 10 15 21 28 36 45
%e A194977    9 13 18 24 31 39 48
%e A194977   14 19 25 32 40 49 59
%t A194977 r = Sqrt[2]; p[n_] := 1 + Floor[n/r]
%t A194977 Table[p[n], {n, 1, 90}]  (* A049474 *)
%t A194977 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194977 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194977 f[20] (* A194976 *)
%t A194977 row[n_] := Position[f[30], n];
%t A194977 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194977 v[n_, k_] := Part[row[n], k];
%t A194977 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194977 {k, 1, n}]] (* A194977 *)
%t A194977 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194977 {n, 1, 80}]] (* A194978 *)
%Y A194977 Cf. A194959, A194976, A194978.
%K A194977 nonn,tabl
%O A194977 1,2
%A A194977 _Clark Kimberling_, Sep 07 2011
%E A194977 Terms a(70) and beyond from _G. C. Greubel_, Mar 28 2018