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A194966 Interspersion fractally induced by A194965, a rectangular array, by antidiagonals.

%I A194966 #9 Oct 18 2021 08:45:31
%S A194966 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,17,22,25,26,27,28,
%T A194966 23,24,29,33,34,35,36,30,31,32,37,42,43,44,45,38,39,40,41,46,52,53,54,
%U A194966 55,47,48,49,50,51,56,63,64,65,66,57,59,60,61,62,58,67,75,76
%N A194966 Interspersion fractally induced by A194965, a rectangular array, by antidiagonals.
%C A194966 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  Every pair of rows eventually intersperse.  As a sequence, A194966 is a permutation of the positive integers, with inverse A194967.
%H A194966 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A194966 Northwest corner:
%e A194966 1...2...4...7...11..16
%e A194966 3...5...8...12..18..25
%e A194966 6...9...13..19..26..34
%e A194966 10..14..20..27..35..44
%e A194966 15..21..28..36..45..55
%t A194966 p[n_] := Floor[(n + 4)/5] + Mod[n - 1, 5]
%t A194966 Table[p[n], {n, 1, 90}]  (* A053824(n+5), n>=0 *)
%t A194966 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194966 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194966 f[20]   (* A194965 *)
%t A194966 row[n_] := Position[f[30], n];
%t A194966 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194966 v[n_, k_] := Part[row[n], k];
%t A194966 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194966 {k, 1, n}]]  (* A194966 *)
%t A194966 q[n_] := Position[w, n]; Flatten[
%t A194966 Table[q[n], {n, 1, 80}]]  (* A194967 *)
%Y A194966 Cf. A194959, A194965, A194967 (inverse).
%K A194966 nonn,tabl
%O A194966 1,2
%A A194966 _Clark Kimberling_, Sep 07 2011