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A194962 Interspersion fractally induced by A194960.

%I A194962 #8 Oct 23 2022 23:26:45
%S A194962 1,2,3,4,5,6,7,9,10,8,11,14,15,12,13,16,20,21,17,18,19,22,27,28,23,25,
%T A194962 26,24,29,35,36,30,33,34,31,32,37,44,45,38,42,43,39,40,41,46,54,55,47,
%U A194962 52,53,48,50,51,49,56,65,66,57,63,64,58,61,62,59,60,67,77,78,68,75,76,69,73,74,70,71,72
%N A194962 Interspersion fractally induced by A194960.
%C A194962 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.
%H A194962 G. C. Greubel, <a href="/A194962/b194962.txt">Antidiagonals n = 0..50, flattened</a>
%e A194962 Northwest corner:
%e A194962    1...2...4...7..11..16..22
%e A194962    3...5...9..14..20..27..35
%e A194962    6..10..15..21..28..36..45
%e A194962    8..12..17..23..30..38..47
%e A194962   18..13..25..33..42..52..63
%e A194962 Antidiagonals of the array:
%e A194962    1;
%e A194962    2,  3;
%e A194962    4,  5,  6;
%e A194962    7,  9, 10,  8;
%e A194962   11, 14, 15, 12, 13;
%e A194962   16, 20, 21, 17, 18, 19;
%e A194962   22, 27, 28, 23, 25, 26, 24;
%e A194962   29, 35, 36, 30, 33, 34, 31, 32;
%e A194962   37, 44, 45, 38, 42, 43, 39, 40, 41;
%t A194962 p[n_] := Floor[(n + 2)/3] + Mod[n - 1, 3]
%t A194962 Table[p[n], {n, 1, 90}]  (* A194960 *)
%t A194962 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194962 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194962 f[20]  (* A194961 *)
%t A194962 row[n_] := Position[f[30], n];
%t A194962 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194962 v[n_, k_] := Part[row[n], k];
%t A194962 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194962 *)
%t A194962 q[n_] := Position[w, n]; Flatten[
%t A194962 Table[q[n], {n, 1, 80}]]  (* A194963 *)
%Y A194962 Cf. A194959, A194960, A194962, A194963.
%K A194962 nonn,tabl
%O A194962 1,2
%A A194962 _Clark Kimberling_, Sep 07 2011