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A194981 Interspersion fractally induced by A194979, a rectangular array, by antidiagonals.

%I A194981 #5 Mar 30 2012 18:57:44
%S A194981 1,2,3,4,6,5,7,10,8,9,11,15,12,14,13,16,21,17,20,18,19,22,28,23,27,24,
%T A194981 25,26,29,36,30,35,31,32,34,33,37,45,38,44,39,40,43,41,42,46,55,47,54,
%U A194981 48,49,53,50,52,51,56,66,57,65,58,59,64,60,63,61,62,67,78,68
%N A194981 Interspersion fractally induced by A194979, a rectangular array, by antidiagonals.
%C A194981 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194981 is a permutation of the positive integers, with inverse A194982.
%e A194981 Northwest corner:
%e A194981 1...2...4...7...11..16..22
%e A194981 3...6...10..15..21..28..36
%e A194981 5...8...12..17..23..30..38
%e A194981 9...14..20..27..35..44..54
%e A194981 13..18..24..31..39..48..58
%t A194981 r = Sqrt[3]; p[n_] := 1 + Floor[n/r]
%t A194981 Table[p[n], {n, 1, 90}]  (* A194979 = 1+ A097337 *)
%t A194981 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194981 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194981 f[20] (* A194980 *)
%t A194981 row[n_] := Position[f[30], n];
%t A194981 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194981 v[n_, k_] := Part[row[n], k];
%t A194981 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194981 {k, 1, n}]]  (* A194981 *)
%t A194981 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194981 {n, 1, 80}]]  (* A194982 *)
%Y A194981 Cf. A194959, A019480, A194982.
%K A194981 nonn,tabl
%O A194981 1,2
%A A194981 _Clark Kimberling_, Sep 07 2011