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A194969 Interspersion fractally induced by A194968, a rectangular array, by antidiagonals. 4

%I

%S 1,2,3,4,6,5,7,10,8,9,11,15,12,13,14,16,21,17,18,20,19,22,28,23,24,27,

%T 25,26,29,36,30,31,35,32,34,33,37,45,38,39,44,40,43,41,42,46,55,47,48,

%U 54,49,53,50,51,52,56,66,57,58,65,59,64,60,61,63,62,67,78,68

%N Interspersion fractally induced by A194968, 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, A194969 is a permutation of the positive integers, with inverse A194970.

%e Northwest corner:

%e 1...2...4...7...11..16

%e 3...6...10..15..21..28

%e 5...8...12..17..23..30

%e 9...13..18..24..31..39

%e 14..20..27..35..44..54

%t r = GoldenRatio; p[n_] := 1 + Floor[n/r]

%t Table[p[n], {n, 1, 90}] (* A019446 *)

%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] (* A194968 *)

%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}]] (* A194969 *)

%t q[n_] := Position[w, n]; Flatten[Table[q[n],

%t {n, 1, 80}]] (* A194970 *)

%Y Cf. A194958, A019446, A194968, A194970.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 07 2011

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Last modified June 13 07:19 EDT 2021. Contains 344981 sequences. (Running on oeis4.)