%I #5 Mar 30 2012 18:57:44
%S 1,3,2,6,5,4,10,9,7,8,15,14,11,13,12,21,20,16,19,18,17,28,27,22,26,25,
%T 24,23,36,35,29,34,33,32,30,31,45,44,37,43,42,41,38,40,39,55,54,46,53,
%U 52,51,47,50,49,48,66,65,56,64,63,62,57,61,60,59,58,78,77,67
%N Interspersion fractally induced by A008621, 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, A194980 is a permutation of the positive integers, with inverse A195081.
%e Northwest corner:
%e 1...3...6...10..15..21..38
%e 2...5...9...14..20..27..35
%e 4...7...11..16..22..29..37
%e 8...13..19..26..34..43..53
%e 12..18..25..33..42..52..63
%t r = 4; p[n_] := 1 + Floor[n/r]
%t Table[p[n], {n, 1, 90}] (* A008621 *)
%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] (* A195079 *)
%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}]] (* A195080 *)
%t q[n_] := Position[w, n]; Flatten[Table[q[n],
%t {n, 1, 80}]] (* A195081 *)
%Y Cf. A008621, A195079, A195081.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Sep 08 2011