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Interspersion fractally induced by A008621, a rectangular array, by antidiagonals.
3

%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