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