A194962 - OEIS

%I #8 Oct 23 2022 23:26:45

%S 1,2,3,4,5,6,7,9,10,8,11,14,15,12,13,16,20,21,17,18,19,22,27,28,23,25,

%T 26,24,29,35,36,30,33,34,31,32,37,44,45,38,42,43,39,40,41,46,54,55,47,

%U 52,53,48,50,51,49,56,65,66,57,63,64,58,61,62,59,60,67,77,78,68,75,76,69,73,74,70,71,72

%N Interspersion fractally induced by A194960.

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.

%H G. C. Greubel, <a href="/A194962/b194962.txt">Antidiagonals n = 0..50, flattened</a>

%e Northwest corner:

%e    1...2...4...7..11..16..22

%e    3...5...9..14..20..27..35

%e    6..10..15..21..28..36..45

%e    8..12..17..23..30..38..47

%e   18..13..25..33..42..52..63

%e Antidiagonals of the array:

%e    1;

%e    2,  3;

%e    4,  5,  6;

%e    7,  9, 10,  8;

%e   11, 14, 15, 12, 13;

%e   16, 20, 21, 17, 18, 19;

%e   22, 27, 28, 23, 25, 26, 24;

%e   29, 35, 36, 30, 33, 34, 31, 32;

%e   37, 44, 45, 38, 42, 43, 39, 40, 41;

%t p[n_] := Floor[(n + 2)/3] + Mod[n - 1, 3]

%t Table[p[n], {n, 1, 90}]  (* A194960 *)

%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]  (* A194961 *)

%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}, {k, 1, n}]]  (* A194962 *)

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

%t Table[q[n], {n, 1, 80}]]  (* A194963 *)

%Y Cf. A194959, A194960, A194962, A194963.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 07 2011