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A194974 Interspersion fractally induced by A194973, a rectangular array, by antidiagonals.

%I A194974 #5 Mar 30 2012 18:57:44
%S A194974 1,2,3,4,5,6,7,8,9,10,11,13,14,15,12,16,19,20,21,17,18,22,26,27,28,23,
%T A194974 24,25,29,34,35,36,30,31,32,33,37,43,44,45,38,40,41,42,39,46,53,54,55,
%U A194974 47,50,51,52,48,49,56,64,65,66,57,61,62,63,58,59,60,67,76,77
%N A194974 Interspersion fractally induced by A194973, a rectangular array, by antidiagonals.
%C A194974 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.
%e A194974 Northwest corner:
%e A194974 1...2...4...7...11
%e A194974 3...5...8...13..19
%e A194974 6...9...14..20..27
%e A194974 10..15..21..28..36
%e A194974 12..17..23..30..38
%t A194974 p[n_] := Floor[(n + 3)/4] + Mod[n - 1, 4]
%t A194974 Table[p[n], {n, 1, 90}]  (* A053737(n+4), n>=0 *)
%t A194974 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194974 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194974 f[20]  (* A194973 *)
%t A194974 row[n_] := Position[f[30], n];
%t A194974 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194974 v[n_, k_] := Part[row[n], k];
%t A194974 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194974 {k, 1, n}]]  (* A194974 *)
%t A194974 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194974 {n, 1, 80}]]  (* A194975 *)
%Y A194974 Cf. A194959, A194973, A194975.
%K A194974 nonn,tabl
%O A194974 1,2
%A A194974 _Clark Kimberling_, Sep 07 2011